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- Discussion Type
- discussion topictorsion
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jul 5th 2011

I have tried to make the page torsion look more like a disambiguation page and less like a mess. But only partially successful.

- Discussion Type
- discussion topicquasi-state
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 30th 2011

stub for quasi-state

- Discussion Type
- discussion topicWigner's theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 30th 2011

stub for Wigner’s theorem

- Discussion Type
- discussion topicdiffeological oo-groupoid
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jun 29th 2011

I have split off from smooth infinity-groupoid – structures the section on concrete objects, creating a new entry concrete smooth infinity-groupoid.

Right now there is

a proof that 0-truncated concrete smooth $\infty$-groupoids are equivalent to diffeological spaces;

and an argument that 1-truncated concrete smooth $\infty$-groupoids are equivalent to “diffeological groupoids”: groupoids internal to diffeological spaces.

That last one may require some polishing.

I am still not exactly sure where this is headed, in that: what the deep theorems about these objects should be. For the moment the statement just is: there is a way to say “diffeological groupoid” using just very ygeneral nonsense.

But I am experimenting on this subject with Dave Carchedi and I’ll play around in the entry to see what happens.

- Discussion Type
- discussion topicFunctorial analysis
- Category Latest Changes
- Started by fpaugam
- Comments 3
- Last comment by TobyBartels
- Last Active Jun 27th 2011

- I have introduced a new section in nlab intitled functorial analysis.

It talks about the functor of point approach to functional analysis, using partially defined functionals.

- Discussion Type
- discussion topicclassifying objects toc
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jun 27th 2011

I thought about starting a floating toc for classifying objects and related, but then decided to subsume it into Yoneda lemma - contents. There I have now added the list of entries

and, conversely, included that toc into all these entries.

- Discussion Type
- discussion topicumbrella category
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Jun 27th 2011

have split off the definition of umbrella category from subterminal object

- Discussion Type
- discussion topicn-topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 26th 2011

since the link was requested somewhere, I have created a stub for n-topos

- Discussion Type
- discussion topicconvenient category of topological spaces
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Todd_Trimble
- Last Active Jun 25th 2011

In convenient category of topological spaces, I rewrote a little under the section on counterexamples, and I added a number of examples and references. Some of this came about through a useful exchange with Alex Simpson at MO, here.

- Discussion Type
- discussion topicTubular Neighbourhoods in Mapping Spaces
- Category Latest Changes
- Started by Andrew Stacey
- Comments 3
- Last comment by Andrew Stacey
- Last Active Jun 22nd 2011

I got a question by email about the

*equivariant*tubular neighbourhoods in loop spaces (as opposed to those defined using propagating flows so I figured it was time to nLabify that section of differential topology of mapping spaces. Of course, in so doing I figured out a generalisation: given a fibre bundle $E \to B$, everything compact, we consider smooth maps $E \to M$ which are constant on fibres. This is a submanifold of the space of all smooth maps $E \to M$. Assuming we can put a suitable measure on the fibres of $E$, then we can define a tubular neighbourhood of this submanifold.Details at equivariant tubular neighbourhoods. Title may be a bit off now, but it’s that because the original case was for the fibre bundle $S^1 \to S^1$ with fibre $\mathbb{Z}_n$.

This entry is also notable because I produced it using a whole new LaTeX-to-iTeX converter. Details on the relevant thread.

- Discussion Type
- discussion topicTomita-Takesaki modular flow
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jun 20th 2011

I added a reference to a paper of Connes and Rovelli (1994) and a link (in modular theory) to

- MathOverflow question tomita-takesaki-versus-frobenuis-where-is-the-similarity

where André Henriques asks about some Connes philosophy. But André quotes in explaining the background to his question, that in full generality there is a homomorphism from imaginary line into the 2-group of invertible bimodules of the given von Neumann algebra $M$, which

*in the presence of state*lifts to the homomorphism into $Aut(M)$. I learned just the case when there is a state, and am delighted to hear that this is just a strengthening of some categorical structure which exists even more generally. If somebody is familiar or can dig more on that general case, it would be nice to have such categorical picture in the $n$Lab entry modular theory.

- Discussion Type
- discussion topicStanford Enc, of Philosphy; quantum mechanics
- Category Latest Changes
- Started by zskoda
- Comments 7
- Last comment by zskoda
- Last Active Jun 20th 2011

- Stanford Encyclopaedia of Philosophy online, contents is free online in the article by article html format (for now, they pledge for support to stay so…) ! Good quality stuff online. I added the link to philosophy, and will later add it to math archives.

Specially good for usage and references in our foundational entries on quantum mechanics is that they have excellent online articles quantum logic and probability theory, quantum mechanics: Kochen-Specker theorem, quantum mechanics and quantum mechanics: von Neumann vs. Dirac.

- Discussion Type
- discussion topicDiaconescu's theorem
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by Urs
- Last Active Jun 20th 2011

Igor Bakovic created Diaconescu’s theorem

- Discussion Type
- discussion topicPDEs, Jet D-modules and exterior differential systems
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Jun 19th 2011

you may recall (okay, probably not ;-) what I once wrote in the entry on exterior differential systems: while in the classical literature these are thought of as dg-ideals in a de Rham complex, we should think of them as sub-Lie algebroids of tangent Lie algebroids.

Since exterior differential systems over X encode and are encoded by partial differential equations on functions on X, this means that such sub-Lie algebroids are partial differential equations.

This perspective is amplified much more in the literature on D-modules: I think we can think of a D-scheme as an infinite-order analog of a Lie algebroid, which is the corresponding first-order notion. The Jet-bundle with its D-scheme structure is the infinite-order analog of the tangent Lie algebroid.

And sub-D-schemes of Jet-D-schemes are partial differential equations, this is what everyone on D-geometry tells you first.

So I think there is a nice story here.

- Discussion Type
- discussion topicUpdate to BV formalism
- Category Latest Changes
- Started by fpaugam
- Comments 3
- Last comment by zskoda
- Last Active Jun 19th 2011

- I have updated the reference section on BV formalism by the following:

i think the Beilinson-Drinfeld book does not treat the classical BV formalism in full generality, even if

they give a natural language to formalize this (pseudo-tensor, i.e., local operations).

I changed the corresponding references by saying they give a formalism for quantum BV on algebraic curves.

The general quantum BV formalism is being studied by Costello-Gwilliam and the formalism of chiral algebras

in higher dimension that has to be used to generalize Beilinson-Drinfeld to higher dimension is being studied

by Gaitsgory-Francis in their Chiral Koszul duality article (using infinity categorical localizations to replace model category

tools for homotopy theory, that are not directly available).

I also precised the reference to my article about this that uses the language of Beilinson-Drinfeld book and particularly

local operations, to deal with classical BV formalism for general gauge theories. Beilinson-Drinfeld only treat the

classical BRST formalism and not classical BV i think (at least not for general base manifold, only for curves).

- Discussion Type
- discussion topicaffiliated element
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jun 19th 2011

New entry affiliated operator of a $C^\ast$-algebra aka affiliated element. This is important for the circle of entries on algebraic QFT, as the operator algebras are formed by bounded operators, while we typically need unbounded operators like derivative operator to do quantum mechanics.

I sent a version of that entry but the $n$Lab stuck in the middle of the operation so I am not sure if I succeeded. So here is the copy:

## Motivation

Most of the applications of operator algebras stuck in the problem that (hermitean or not) unbounded operators do not form an algebra under composition (or under Jordan multiplication); while the algebras of bounded operators are insufficient as most of applications involve also unbounded operators like the partial derivative operator on $L^2(\mathbb{R}^n)$ which is proportional to the momentum operator in quantum mechanics.

## Idea

The motivational problem is typically resolved by considering an operator algebra which contains operators which properly approximate the unbounded operators as close as one wishes, and formalize this by defining the larger class of “approximable” operators by means of operator algebra itself. One way to do this is to define the

**affiliated elements**of $C^\ast$-algebra, or the operators affiliated with the $C^\ast$-algebra. The idea is that if there is an unbounded self-adjoint operator then we can consider its spectral projections; they are bounded and if we include them into the algebra, the convergence of the spectral decomposition will supply the approximation.## Literature

- S. L. Woronowicz, K. Napiórkowski,
*Operator theory in $C^\ast$-framework*, Reports on Mathematical Physics**31**, Issue 3 (1992), 353-371, doi, pdf - S. L. Woronowicz,
*$C^\ast$-algebras generated by unbounded elements*, pdf - wikipedia affiliated operator

- S. L. Woronowicz, K. Napiórkowski,

- Discussion Type
- discussion topicinfinitesimal cohesion (formal cohesion)
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Jun 17th 2011

I was forced to split off the section on infinitesimal cohesion from the entry cohesive (infinity,1)-topos – because after I had expanded it a little more, the nLab server was completely refusing to safe the entry (instead of just being absurdly slow with doing so). I guessed that it is was its length that caused the software to choke on it, and it seems I was right. The split-off subsection is now here:

cohesive (infinity,1)-topos – infinitesimal cohesion

Things I have edited:

added a bried Idea-paragraph at the beginning;

changed the terminology from “$\infty$-Lie algebroid” to “formally cohesive infinity-groupoid” , making the former a special case (first order) of the latter;

expanded the definition of formal smoothness, added remarks on formal unramifiedness in the $\infty$-context.

- Discussion Type
- discussion topicCleaned out the Sandbox
- Category Latest Changes
- Started by Andrew Stacey
- Comments 1
- Last comment by Andrew Stacey
- Last Active Jun 17th 2011

I wanted to test something in the Sandbox (for this question of David Roberts on the TeX Stackexchange) and it was looking a bit cluttered so I gave it a clean-out.

- Discussion Type
- discussion topicD-scheme
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by zskoda
- Last Active Jun 17th 2011

I am about to create D-scheme, but currently the Lab is down and the server does not react to my login attempts…

- Discussion Type
- discussion topicChiral Algebras
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jun 17th 2011

I am starting a linked keyword list at Chiral Algebras

- Discussion Type
- discussion topicQuasi-Coherent Sheaves And Tannaka Duality Theorems
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Jun 17th 2011

created Reference-entry for the new Quasi-Coherent Sheaves and Tannaka Duality Theorems and am adding pointers to it to the relevant entries now.

- Discussion Type
- discussion topicjet bundles and de Rham space technology
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jun 17th 2011

I am about to write something at jet bundle and elsewhere about the general abstract perspective.

In chapter 2 of Beilinson-Drinfeld’s Chiral Algebras they have the nice characterization of the Jet bundle functor as the right adjoint to the forgetful functor $F : Scheme_{\mathcal{D}}(X) \to Scheme(X)$ from D-schemes over $X$ to just schemes over $X$.

Now, since D-modules on $X$ are quasicoherent modules on the de Rham space $\Pi_{inf}(X)$, I guess we can identify

$Scheme_{\mathcal{D}}(X)$with

$Schemes/\Pi_{inf}(X)$and hence the forgetful functor above is the pullback functor

$\array{ F(E) &\to& E \\ \downarrow && \downarrow \\ X &\to& \Pi_{inf}(X) }$aling the lower canonical morphism (“constant infinitesimal path inclusion”).

This would mean that we have the following nice general abstract characterization of jet bundles:

let $\mathbf{H}$ be a cohesive (infinity,1)-topos equipped with infinitesimal cohesion $\mathbf{H} \hookrightarrow \mathbf{H}_{th}$. For any $X \in \mathbf{X}$ we then have the canonical morphism $i : X \to \mathbf{\Pi}_{inf}(X)$.

The

$Jet := (i^* \dashv i_*) : \mathbf{H}/X \to \mathbf{H}/\mathbf{\Pi}(X)$**Jet bundle functor**is then simply the corresponding base change geometric morphismor rather, if we forget the $\mathcal{D}$-module structure on the coherent sheaves on the jet bundle, it is the comonad $i^* i_*$ induced by that.

Does that way of saying it ring a bell with anyone?

- Discussion Type
- discussion topicCech cocycles for differential characteristic classes
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jun 16th 2011

on my personal web I have created an entry Cech cocycles for differential characteristic classes (schreiber).

This is a Reference-entry for the article that I wrote with Domenico and Jim. The point is to keep a hyperlinked abstract and a pdf of the article (which contains more than the current arXiv version).

- Discussion Type
- discussion topicdiscrete infinity-groupoid
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jun 16th 2011

for completeness I think there is a point in having an entry discrete infinity-groupoid. So I have created it.

(We already had discrete group with the same purpose.)

- Discussion Type
- discussion topicgeneralized second law of thermodynamics
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 15th 2011

- Discussion Type
- discussion topictwisted differential c-structures
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 15th 2011

I am starting an entry twisted differential c-structures. This is supposed to eventually contain the general statements of which statements in the following entries are special cases:

- Discussion Type
- discussion topicdifferential T-duality
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 15th 2011

I am starting an entry differential T-duality. This is supposed to eventually contain the technical details that are currently hidden in th Reference-entry T-Duality and Differential K-Theory

- Discussion Type
- discussion topicWasserstein metric
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 14th 2011

stub for Wasserstein metric

- Discussion Type
- discussion topicFHT-theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jun 14th 2011

started a Reference entry FHT theorem with a brief rough statement of what the theorem says. For the moment mainly in order to include pointers to where in the three articles the theorem is actually hidden (I think it is hidden quite well… ;-)

- Discussion Type
- discussion topicinformation geometry
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Jun 14th 2011

I am hereby moving the following discussion from information geometry to here:

Tim Porter: I have looked briefly at the Methods of Info Geom book and it seemed to me to be distantly related to what the eminent statistician David Kendall used to do. He and some coauthors wrote a very nice book called: Shape and Shape Theory (nothing to do with Borsuk’s Shape Theory). The theory may be of relevance as it used differential geometric techniques. (Incidently there are some nice questions concerning the space of configurations of various types that would be a good source for student project work in it.)

My query is whether the link is a strong one between the Amari stuff and those Kendall Shape space calculations. Kendall’s theory and some similar work by Bookstein is widely used in identifcation algorithms using a feature space. In case the link is only faint I will leave it at that for the moment. Any thoughts anyone?

Eric: I wrote some stuff here, which is now relegated to Revision 5. I’ve rewritten most of the material here.

- Discussion Type
- discussion topicreductions deformations resolutions in physics
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Jun 13th 2011

Igor Khavkine is starting an entry reductions deformations resolutions in physics

this is based on seminar notes for talks that he is currently giving

- Discussion Type
- discussion topiccoexponential map
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jun 12th 2011

New entry coexponential map, redirecting symmetrization map. It accompanies today’s entry hyper-envelope of a Lie algebra which hopefully precedes my writing up of a proof of alternative realizations of the hyper-envelope.

- Discussion Type
- discussion topicLandau-Ginzburg model
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jun 10th 2011

stub for Landau-Ginzburg model

- Discussion Type
- discussion topiclocalization of an abelian category
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Jun 8th 2011

I have started a stub localization of an abelian category. Added a list of related terms at topologizing subcategory.

- Discussion Type
- discussion topiccoisotropic submanifold
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 8th 2011

started coisotropic submanifold

- Discussion Type
- discussion topicalgebra spectrum
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jun 7th 2011

started a stub for algebra spectrum

- Discussion Type
- discussion topicOrthogonal structure
- Category Latest Changes
- Started by Andrew Stacey
- Comments 2
- Last comment by Urs
- Last Active Jun 6th 2011

On the basis of wikilinking everything, I discovered that orthogonal structure didn’t exist, so I created it. Being me, I gave it my infinite dimensional slant. Clearly there’s lots that could be said here, so it’s a middling stub.

- Discussion Type
- discussion topicPropagating flows
- Category Latest Changes
- Started by Andrew Stacey
- Comments 12
- Last comment by Andrew Stacey
- Last Active Jun 6th 2011

First stab at propagating flows (highly tempted to put in a redirect for

*propogating*flows). I wrote it without reference to either my article or Veroniques’ in the hope that by being forced to look at it afresh, I’d get the argument right. I’m not convinced that I managed it so I’ll need to polish it considerably.

- Discussion Type
- discussion topicReconstruction of Groups
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Jun 5th 2011

Article page (unfinished but already has a sensible story) Reconstruction of Groups.

- Discussion Type
- discussion topicmapping space - contents
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Andrew Stacey
- Last Active Jun 3rd 2011

created TOC mapping space - contents and added it as “floating TOC” to relevant entries.

Andrew, please check which of your entires on mapping spaces are still missing, if any. What’s the status of your project differential topology of mapping spaces?

- Discussion Type
- discussion topicC-k topology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 2nd 2011

stubby stub for Whitney C-k topology

- Discussion Type
- discussion topicstable derivator
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Mike Shulman
- Last Active Jun 2nd 2011

I have added reference pointers to Moritz Groth’s document on “Derivators, pointed derivators and stable derivators” to the relevant entries, such as stable derivator.

Mike, I forget if you mentioned that before or not. I only learned of his work today. Part of his PhD thesis with Schwede.

- Discussion Type
- discussion topicpath integral as a pull-push transform
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active May 31st 2011

I badly need to polish the $n$Lab entries related to path integrals. Today a student asked me how the pull-push operation in string topology is a remnant of a quantum path integral. So a started writing now

So far there is the description of the archetypical path integral for the quantum particle propagating on the line in terms of pull-tensor-push.

- Discussion Type
- discussion topicdg-algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by zskoda
- Last Active May 31st 2011

I moving the following old discussion from dg-algebra to here:

## Discussion

A previous version of this entry gave rise to the following discussion

+–{.query} Zoran, why would you not say that this is ’following the product rule from ordinary calculus’, as I wrote? Not that this can be proved like the product rule can, but it's an easy mnemonic (and a similar one works for direct sums too). —Toby

I find it very confusing for me at least. The Leibniz rule is about the coproduct in a single algebra; here one has several algebras with different differentials, not a single derivative operators, and not acting on a tensor square of a single algebra, so it is a bit far. If $A=B$ then I would be happy, but otherwise it is too general. —Zoran

You mean that if $A = B$, then the Leibniz rule is a special case of this? Then surely it is also a special case of the more general case without $A = B$? Anyway, I think that it's more an example of categorification than generalisation. —Toby

For some special algebras this is true. For example, the dual of symmetric algebra as a Hopf algebra can be identified with the infinite order formal differential operators with constant coefficients (the isomorphism is given by evaluation at zero). Thus the Leibniz rule for derivatives is indeed the dual coproduct to the product on the symmetric algebras. There are braided etc. generalizations to this, and a version for computing the coproduct on a dual of enveloping algebras. In physics the addition of momenta and angular momenta for multiparticle systems is exactly coming from this kind of coproduct. But in all these cases the operators whose product you are taking live in a representation of a single algebra. — Zoran

=–

- Discussion Type
- discussion topicT-Duality and Differential K-Theory
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by domenico_fiorenza
- Last Active May 31st 2011

I am creating a reference-entry T-Duality and Differential K-Theory. In the course of this I have now first of all created stubs for

- Discussion Type
- discussion topicConstantin Teleman
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 30th 2011

added keyword-indexed references to the entry on Constantin Teleman

- Discussion Type
- discussion topicgeometric realization of cohesive infinity-groupoids
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 30th 2011

just for completeness I have split off an entry geometric realization of cohesive infinity-groupoids, such as to complete a mini-sub-toc:

- Discussion Type
- discussion topichomological QFT
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 30th 2011

started an entry homological quantum field theory

- Discussion Type
- discussion topic[[measurable space]]
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by Urs
- Last Active May 29th 2011

A coupld additions to measurable space that I've been sitting on for a while, and which I've realised that I'm not going to write more clearly anytime soon.

But someday I would like to move a lot of the discussion about various approaches to measure theory and make measurable space itself simpler, with pointers to variations.

- Discussion Type
- discussion topicGoldman bracket
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 28th 2011

created Goldman bracket

- Discussion Type
- discussion topicTannaka duality for Lie groupoids
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 27th 2011

- Discussion Type
- discussion topicspectral cookbook
- Category Latest Changes
- Started by zskoda
- Comments 16
- Last comment by zskoda
- Last Active May 27th 2011

New entry spectral cookbook with sketch of some

*very*nice constructions of A. Rosenberg. New stub sheaf on a noncommutative space, pretty contentless so far, and a redirect page noncommutative sheaf, where the latter may have a different meaning (that is why a separate page).

- Discussion Type
- discussion topicAnonymous Coward
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by TobyBartels
- Last Active May 27th 2011

I have removed this sentence from AnonymousCoward:

(Well, usually. Urs Schreiber —or for all we know, possibly somebody impersonating him (^_^)— has managed to keep his IP address out sometimes.)

This makes it sound as if I did something intentionally to hide my IP, which is not the case. Rather there must be a problem with the software, if something that should not have happened did happen.

I have also removed the following old discussion, which is better had here on the forum:

*Eric*: Can we change this? I am not anonymous, but I also do not want my IP listed (since it resolves to my employer, which I think should be private.) I guess I can always just not post from work, but small distractions now and then are nice.*Toby*: IP addresses are almost always logged by web software, even for readers; in the past, these logs were usually deleted after a while, but now storage space is so cheap that this may no longer be true. People like to have the IP address available in case of problems —spam, DoS attacks, etc—. I like having that sort of information publicly available, rather than tucked into logs that are hidden behind passwords, to prevent the devlopment of hierarchies.But if you want to be anonymous on the web, try searching for ’web proxy’ or the like. However, Jacques's software makes a fair attempt to defeat these, since they are often used to spam. (Even in general, I don't know how well they work, and ultimately

*they*become the people with the secret information.)*Toby*: I see that Urs managed to post from ’from bogus address’ today (June 27). Maybe we should ask him what he did differently!*Eric*: I don’t mind if administrators can see my IP for security reasons, but it is not clear what purpose it serves to actually display it publicly for all to see. For example, I can see the IP addresses of people who comment on my blog, but it is not displayed for everyone to see.*Toby*: That creates a hierarchy (of information if not power, but one leads to the other) where administrators are above everybody else. The wiki way gives the same information to everybody.

- Discussion Type
- discussion topiccopyright
- Category Latest Changes
- Started by zskoda
- Comments 67
- Last comment by zskoda
- Last Active May 26th 2011

New stub copyright both about copyright attitude of the $n$Community and as a place to collect links to interesting analysis of copyright, free literature, protection from plagiarism and similar issues. It also links to citations (zoranskoda).

- Discussion Type
- discussion topicemptypage
- Category Latest Changes
- Started by zskoda
- Comments 9
- Last comment by zskoda
- Last Active May 25th 2011

I created a page emptypage. It would belong to meta category of pages but I do not want to attach even that label to it. I want it empty, I want it orphane, non-aliased and non-classified, truly minimal content and minimal sourcecode page.

With one click of the mouse I call the label of nlab:HomePage in my bookmarks bar, and then I change the URL by hand or go from HomePage to one of the links or use the search from there. If I am on slow connection, sometimes even HomePage loads longer. I think that some other users can smartly use the initial page like that. HomePage has information for newcomers, experienced users can sometimes prefer emptypage as their cleaner and leaner $n$Lab homepage.

So emptypage is a quick way to see that the lab is up with a minimal length page and to get the basis for $n$Lab search window or to change the URL without the cost of the HomePage load and HomePage html display time. Now with HomePage having also an additional

*Terms of usage*section it grown today another bit more, so a reason more to create emptypage and to hopefully leave it empty.I use emptypage to have it easier to type than empty page.

I hope other people won’t find it offending that I created a lean-expert-user depart point without consulting others, but I think it has obvious usages for some and it is not on the way to others, I hope.

- Discussion Type
- discussion topicCartier operator
- Category Latest Changes
- Started by hilbertthm90
- Comments 1
- Last comment by hilbertthm90
- Last Active May 25th 2011

I’ve been thinking a lot about degeneration of Hodge to de Rham spectral sequence lately. I checked out the page on the nlab about it. I saw that there was a link to Cartier operator but no page, so I created it.

This actually got me thinking. In some sense degeneration at $E_1$ is “intrinsic” to the derived category $D(X)$ (I just made that up based on what I wrote in the article). There is a naive way to try to prove that if $X$ and $Y$ are derived equivalent and if the SS degenerates for one, the other should too. I couldn’t see a way to make it work. Is there an obvious reason this should be true, or an obvious counterexample?

- Discussion Type
- discussion topicnoncommutative projective geometry
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by zskoda
- Last Active May 24th 2011

New stubs noncommutative projective geometry and Michael Artin.

- Discussion Type
- discussion topicLax functor
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active May 19th 2011

An anonymous correspondent has put a question on lax functor, or rather has edited a previous query.

- Discussion Type
- discussion topicgeometric surjection/embedding factorization
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 18th 2011

have split off geometric surjection/embedding factorization from the relevant entries. Maybe I find the time to spell out the proof there.

- Discussion Type
- discussion topicB-bordism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 16th 2011

stub for B-bordism – just to record the Manifold Atlas-reference for the moment