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- Discussion Type
- discussion topicPeierls bracket
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 9th 2013

at

*Peierls bracket*I have added a bunch of further references and have slightly expanded the Idea-section

- Discussion Type
- discussion topicgeometric quantization of symplectic groupoids
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Sep 9th 2013

I have split off an entry geometric quantization of symplectic groupoids from symplectic groupoid.

I have also tried to clean up and make more systematic the Idea-section at geometric quantization

- Discussion Type
- discussion topicmotivic quantization -- Expositional survey
- Category Latest Changes
- Started by Urs
- Comments 34
- Last comment by Urs
- Last Active Sep 9th 2013

I have now what should be a readable pre-version of

This still needs a round of polishing or two. But it should be at least readable.

If anyone is interested, have a look, be critical and try to poke holes into it.

- Discussion Type
- discussion topiclattice renormalization
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 9th 2013

added some references to

*lattice field theory*and*lattice renormalization*. Though I am still looking for a reference on the latter that states the basic mechanism clearly…

- Discussion Type
- discussion topicsuperselection sector
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 9th 2013

at

*superselection sector*I tried to state more explicitly the fact that superselection sectors are equivalently the irreps of the algebra of observables in the space of quantum states.Also cross-linked with

*irreducible representation*and with*quantum observable*.

- Discussion Type
- discussion topicNewton's laws of motion
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 8th 2013

over at

*prequantized Lagrangian correspondence*I needed to point to Newton’s laws, so I have started an entry*Newton’s laws of motion*. So far mainly it just contains briefly the content of Newton’s laws in modern language.

- Discussion Type
- discussion topicmotivating quantum mechanics from classical mechanics + Lie theory
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by Urs
- Last Active Sep 5th 2013

prompted by this physics.SE question I ended up adding to Idea-section of the entry

*quantization*a new subsection titled*Motivation from classical mechanics and Lie theory*.

- Discussion Type
- discussion topicLocal sections
- Category Latest Changes
- Started by DavidRoberts
- Comments 22
- Last comment by TobyBartels
- Last Active Sep 4th 2013

Changed the page local section to discuss a slightly more general concept than the local sections of a bundle, and over a more general pretopology.

- Discussion Type
- discussion topicF4
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 2nd 2013

added some references on representationology of $F_4$ to

*F4*

- Discussion Type
- discussion topicgeometric representation theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by David_Corfield
- Last Active Sep 2nd 2013

added to

*geometric representation theory*a quote of program description of the MSRI program next year.

- Discussion Type
- discussion topicworldvolume/target supersymmetry of brane sigma-models -- table
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by TobyBartels
- Last Active Sep 1st 2013

had need for a small table

*worldvolume-target supersymmetry of brane sigma-models*and so I created one. Have included it into the relevant entries.Also created a stub for

*superembedding approach*, the middle entry of the table.(An nForum issue: as of late I get to see the nForum

*only*in its plain HTML-form, which is very inconvenient. Is this a problem just on my side, or does anyone else experience this?)

- Discussion Type
- discussion topicPseudocompact algebras
- Category Latest Changes
- Started by Tim_Porter
- Comments 6
- Last comment by zskoda
- Last Active Aug 31st 2013

As we were discussing profinite completions the other day in another thread I thought I would add in some points about completed group algebras at profinite group and add some mention of pseudo compact algebras to the pre-existing entry on pseudocompact rings.

It is not clear to me what the connection between these algebras and profinite algebras should be. These pseudocompact and related linear compact algebras use finite dimensionality instead of finiteness to get a sort of algebraic compactness condition.

- Discussion Type
- discussion topicsuper Poincare Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Aug 30th 2013

created super Poincare Lie algebra

linked to it from super Euclidean group and from supergravity

- Discussion Type
- discussion topicPolchinski: String theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 29th 2013

I have Polchinski’s textbook a category:reference-entry

*String theory*, for purposes of better linking to it

- Discussion Type
- discussion topichigher spin geometry - contents
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by David_Corfield
- Last Active Aug 29th 2013

started a topic cluster table of contents

*higher spin geometry - contents*and included it as a “floating table of contents” into relevant entries

- Discussion Type
- discussion topicLocus
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Aug 29th 2013

Started locus following this discussion.

Should left exact localization link to reflective sub-(infinity,1)-category?

- Discussion Type
- discussion topicReferences to differential cohomology in a cohesive topos
- Category Latest Changes
- Started by DavidRoberts
- Comments 3
- Last comment by DavidRoberts
- Last Active Aug 29th 2013

I added a link to the published version of my notes on universal simplicial bundles, here on Urs’ web.

- Discussion Type
- discussion topiccharge conjugation matrix
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 28th 2013

brief remark

*charge conjugation matrix*, just because I needed to be able to point to it

- Discussion Type
- discussion topicsuper translation Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 28th 2013

added little bit more to

*super translation Lie algebra*, including a remark that it is a central extension of the superpoint, regarded as an abelian super Lie algebra.

- Discussion Type
- discussion topicFive lectures on supersymmetry
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 28th 2013

started a hyperlinked index for Dan Freed’s

*Five lectures on supersymmetry*(might use this in a course later this year…)

- Discussion Type
- discussion topictopological M2 on G2-manifolds
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 27th 2013

I only noticed now that the discussion around equation (2.14) in

- Ling Bao, Viktor Bengtsson, Martin Cederwall, Bengt Nilsson,
*Membranes for Topological M-Theory*(arXiv:hep-th/0507077)

identifies the exceptional super Lie algebra $(2+2)$cocycle on $\mathfrak{siso}(7)$ (given by the brane scan) with the “topological membrane” of “topological M-theory”.

I added a brief remark to this extent to

*topological membrane*and updated*brane scan*accodingly. Hope to be expanding on this soon…- Ling Bao, Viktor Bengtsson, Martin Cederwall, Bengt Nilsson,

- Discussion Type
- discussion topicSymplectic group
- Category Latest Changes
- Started by DavidRoberts
- Comments 3
- Last comment by TobyBartels
- Last Active Aug 26th 2013

I created a small page for compact symplectic group, which is not the same as the symplectic group, and added some sentences at both to disambiguate. I’m also working on an entry orthogonal group of an inner product space, which will give the general treatment that covers $O(n)$, $U(n)$ and $Sp(n)$ (and other cases of mixed signature, like $O(n,m)$).

There are interesting charts for $O(n,\mathbb{K})$ using its Lie algebra (in fact various tangent spaces) which don’t come from the exponential mapping, and my aim is to get a reasonably full treatment of these in there.

- Discussion Type
- discussion topicDisjoint sets
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Aug 26th 2013

I added to disjoint subsets.

- Discussion Type
- discussion topicthe Elephant, fully indexed for you
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Mike Shulman
- Last Active Aug 24th 2013

started an index at Elephant

just a tiny beginning. we have entries for many keywords already.

- Discussion Type
- discussion topicKontsevich formality
- Category Latest Changes
- Started by Kevin Lin
- Comments 7
- Last comment by jim_stasheff
- Last Active Aug 23rd 2013

Added stub for Kontsevich formality.

Also added some comments to the HKR page.

- Discussion Type
- discussion topicmicro-causality
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 22nd 2013

I have added to

*microcausality*a quote with a nice discussion. That also cites experimental bounds. But back from the 1970s only – there must be better ones by now.Does anyone happen to know a citation for better experimental bounds, or else might anyone enjoy googling for it? I am out of googlin time now, but I am entertaining myself with advertizing this as an “experimental bound on higher category theory in fundamental physics”, along the lines of the story here.

- Discussion Type
- discussion topic[[partition]]
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by Todd_Trimble
- Last Active Aug 21st 2013

At partition, I've defined partitions of sets, numbers, intervals, measure spaces, and unity on topological spaes, giving these all as special cases of a general concept defined in a monoid whose nonzero elements form an ideal (and possibly equipped with some notion of infinite sum).

- Discussion Type
- discussion topicsome stubs
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 21st 2013

for the exposition at

*motivic quantization*(not done yet) I need some keywords being hyperlinked which don’t really have entries yet. So I created some stubs, to be filled with genuine life later, e.g.and maybe more which I forget. But have to run now. More later.

- Discussion Type
- discussion topicGrothendieck-Teichmüller group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 19th 2013

lightning remark here on Willwacher’s identification of the GT Lie algebra with $H^0$ of the graph complex

- Discussion Type
- discussion topicsplit support
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Aug 18th 2013

New page: split support

- Discussion Type
- discussion topicGoedel incompleteness via hyperdoctrines
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by Todd_Trimble
- Last Active Aug 18th 2013

I wrote up a brief little note on this on my web. Comments are very welcome. This could be transported to the nLab if one wants.

- Discussion Type
- discussion topicWhitehead's principle
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Aug 18th 2013

Added some remarks about Whitehead’s principle as a foundational axiom to Whitehead’s theorem.

- Discussion Type
- discussion topicKuo Tsai Chen
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by jim_stasheff
- Last Active Aug 17th 2013

surprised that we didn’t have this “people”-entry before, now we do:

*Kuo Tsai Chen*

- Discussion Type
- discussion topicamenable topological groupoid
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by DavidRoberts
- Last Active Aug 15th 2013

created

*amenable topological groupoid*. Skipped the definition (gave a pointer, though), just wanted to quickly record that the convolution algebras of amenable groupoids are in the bootstrap category. Added that proposition also there.

- Discussion Type
- discussion topicnew entries
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by Todd_Trimble
- Last Active Aug 14th 2013

Wrote recursive subset and partial recursive function. Not much more than stubs.

- Discussion Type
- discussion topicbootstrap category
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 14th 2013

created

*bootstrap category*

- Discussion Type
- discussion topicK-theory of groupoids/geometric stacks
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 14th 2013

stub for

*groupoid K-theory*, for the moment just to record some pointers

- Discussion Type
- discussion topicmodelizer
- Category Latest Changes
- Started by Zhen Lin
- Comments 25
- Last comment by DavidRoberts
- Last Active Aug 13th 2013

Created modelizer. It’s not clear to me exactly what Grothendieck is taking as a property or as a structure in his definitions, but I tried to make a guess.

- Discussion Type
- discussion topicWitten genus and tmf
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 12th 2013

at

*Witten genus*I have tried to give a more complete list of pointers to the story of refining the Witten genus to a map of $E_\infty$-ring spectra. Now the references there read as follows:

The refinement of the Witten genus from values in modular forms to topological modular forms and further to a morphism of E-∞ rings, hence to the string orientation of tmf is due to

Michael Hopkins,

*Topological modular forms, the Witten Genus, and the theorem of the cube*, Proceedings of the International Congress of Mathematics, Zürich 1994 (pdf)Michael Hopkins,

*Algebraic topology and modular forms*, Proceedings of the ICM, Beijing 2002, vol. 1, 283–309 (arXiv:math/0212397)Matthew Ando, Michael Hopkins, Charles Rezk,

*Multiplicative orientations of KO-theory and the spectrum of topological modular forms*, 2010 (pdf) {#AndoHopkinsRezk}

see also remark 1.4 of

- Paul Goerss,
*Topological modular forms (after Hopkins, Miller and Lurie)*(pdf).

and for more on the sigma-orientation see

- Matthew Ando,
*The sigma orientation for analytic circle-equivariant elliptic cohomology*, Geom. Topol. 7 (2003) 91-153 (arXiv:math/0201092)

Similar additions I have made to

*topological modula form*(which is otherwise an empty entry, alas) and to*tmf*itself.

- Discussion Type
- discussion topicsymplectic topology, Dusa McDuff
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Aug 12th 2013

An updated version of the book

**J-holomorphic Curves and Quantum Cohomology**can be found on the web page of Dusa McDuff which is linked at the new entry Dusa McDuff ! I also started a stub symplectic topology and just a little longer one for Floer homology.

- Discussion Type
- discussion topiccategory of correspondences
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 12th 2013

brief note at

*category of correspondences*on*limits and colimits*.

- Discussion Type
- discussion topiccountable ordinal
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Todd_Trimble
- Last Active Aug 11th 2013

Created a new article, countable ordinal.

- Discussion Type
- discussion topicDirac induction
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 10th 2013

created

*Dirac induction*with a brief note on the relation to the orbit method, via FHT-II.

- Discussion Type
- discussion topictoo simple to be simple
- Category Latest Changes
- Started by Mike Shulman
- Comments 4
- Last comment by TobyBartels
- Last Active Aug 9th 2013

I have added

- The empty function to the empty set is not a constant function.

- Discussion Type
- discussion topicbivariant cohomology theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 6th 2013

*bivariant cohomology theory*, in order to record some references

- Discussion Type
- discussion topicsimplicial bar construction
- Category Latest Changes
- Started by Zhen Lin
- Comments 8
- Last comment by Mike Shulman
- Last Active Aug 4th 2013

I started a page about the simplicial bar construction. I haven’t checked all the details carefully (especially regarding $\mathcal{V}$-naturality!) though.

- Discussion Type
- discussion topicdiscrete objects and cohomology
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Todd_Trimble
- Last Active Jul 28th 2013

added a brief remark to

*discrete object*in a new section*Examples — in infintiy-toposes*on the relation between discreteness and cohomology.This is a (fairly trivial) comment on Mike’s discussion over on the HoTT blog, linked to from the above.

- Discussion Type
- discussion topicMotivic cohomology
- Category Latest Changes
- Started by Marc Hoyois
- Comments 1
- Last comment by Marc Hoyois
- Last Active Jul 21st 2013

Lots of changes at motivic cohomology.

The stuff about the homotopy localization of the Nisnevich (∞,1)-topos I will move to A1-homotopy theory where it more properly belongs.

- Discussion Type
- discussion topicNisnevich site
- Category Latest Changes
- Started by Marc Hoyois
- Comments 5
- Last comment by Marc Hoyois
- Last Active Jul 21st 2013

I decided to add some content to the motivic pages here on the nLab.

I started with Nisnevich site. More to come soon…

- Discussion Type
- discussion topiccompactification
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Jul 21st 2013

at

*compactification*I added in the second sentence of the Idea-section a pointer to*one-point compactification*, to have that mentioned before then the next line starts talking about more general situations.(prompted by this physics.SE question)

- Discussion Type
- discussion topic"B. Blackadar"-s
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by TobyBartels
- Last Active Jul 21st 2013

trivia, but I just ran into this:

I noticed we have entries:

and

both of them referring to operator algebraists. First I thought we need to merge these entries. But after looking around I guess these are indeed two different people. (The German Wikipedia claims here that the second initial of the author of

*K-Theory for Operator Algebras*is “E” not “A”).(Notice that the second entry is mistaken, where it says “Home page” it points not to some author’s home page but to the nLab home page…)

Just making sure. Sorry for the distraction.

- Discussion Type
- discussion topiciterated integral
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Jul 21st 2013

stub for

*iterated integral*(more references as soon as the nLab wakes up again…)

- Discussion Type
- discussion topicTQFT, Nonlocal Operators, and Gapped Phases of Gauge Theories
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 20th 2013

I was starting to make some notes on the new article by Sergei Gukov and Anton Kapustin, at a new “reference”-categorized entry titled

*Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories*But so far there is just a vague indication of the main thrust. I want to flesh out more detail later. On the other hand, tomorrow morning I’ll be going on a two week vacation, so this plan will encounter delays.

- Discussion Type
- discussion topicordinary homology via infinity-modules
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 20th 2013

For the sake of illustration I have added to

*ordinary homology*a section*In terms of higher linear algebra*.Currently the main point is to record, after some preliminaries, the standard observation plus detailed proof that for $X$ a topological space, its ordinary chain complex of singular simplices is, up to equivalence, the $\infty$-colimit of the tensor unit local system with coefficients in $H k Mod$. (Its “$Hk$-Thom spectrum”.)

- Discussion Type
- discussion topiccompacta
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Jul 20th 2013

In the section compacta as algebras, I have written out complete details of a proof that compact Hausdorff spaces are monadic over sets.

- Discussion Type
- discussion topicstable map
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 19th 2013

concerning

*stable map*: is there some nice abstract characterization? Something involving maybe the words “faithful functor of étale groupoids”?

- Discussion Type
- discussion topicmodel structure on (co)chain complexes
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Jul 19th 2013

Added a section with a little bit of detail on model structures on cochain complexes in non-negative degree to model structure on chain complexes.

- Discussion Type
- discussion topiclocalizer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2013

*localizer*, just for completeness

- Discussion Type
- discussion topicHitchin connection
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 17th 2013

- Discussion Type
- discussion topicHermitian structure
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 17th 2013

created a minimum at

*Hermitian structure*.Also edited and expanded the Idea- section at

*Käher structure*a bit.