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- 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 topictaut functor
- Category Latest Changes
- Started by Todd_Trimble
- Comments 2
- Last comment by Mike Shulman
- Last Active Aug 3rd 2013

Made a start on taut functor. Mike, I mentioned your work with Cruttwell on generalized multicategories in a section on applications.

- 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.

- Discussion Type
- discussion topiccompact closed 2-category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2013

stub for

*compact closed 2-category*to accomodate a pointer to Mike Stay’s recent article

- Discussion Type
- discussion topicPoincare duality algebra
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jul 16th 2013

I am starting an entry

*Poincaré duality algebra*, but it still needs some attention

- Discussion Type
- discussion topicunitisation of C-star algebras
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2013

created

*unitisation of C*-algebras*

- Discussion Type
- discussion topicchiral ring
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 16th 2013

stub for

*chiral ring*(not good yet)

- Discussion Type
- discussion topicTarski-Seidenberg theorem
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Jul 14th 2013

I began to expand Tarski-Seidenberg theorem (formerly a stub) by including some commentary on its significance, and some related results. This is to help create a niche for Schanuel’s conjecture, yet to be written, but which was invoked in a discussion at MO.

- Discussion Type
- discussion topicmetaplectic correction
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 14th 2013

stub for

*metaplectic correction*

- Discussion Type
- discussion topicKodaira vanishing theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 12th 2013

brief statement of

*Kodaira vanishing theorem*for the complex geometry case

- Discussion Type
- discussion topicequivariant KK-theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 12th 2013

started a stub

*equivariant KK-theory*with some quick notes. But still very stubby.

- Discussion Type
- discussion topichomotopy colimit
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Andrew Stacey
- Last Active Jul 10th 2013

Wrote a section General weighted colimit formula at homotopy colimit

giving a general formula

spelling out the special case of simplicial diagrams, that reproduces the Bousfield-Kan formula

spelling out the special case of pushout diagrams, that reproduces the formula (or its dual) discussed more in detail in the other examples that were already present

- Discussion Type
- discussion topiccrossed product c*-algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 9th 2013

I tried to collect some references at

*crossed product C*-algebra*on their relation to convolution C*-algebras of action groupoids. But I guess I run out of steam…

- Discussion Type
- discussion topicanalytic assembly map
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 9th 2013

while writing

*Baum-Connes conjecture*I happened to add some stuff to*analytic assembly map*.

- Discussion Type
- discussion topicdirect image with compact supports
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jul 7th 2013

I have added a new paragraph to direct image about direct image functor with compact support $f_! F$. Eventually I would create a separate entry direct image with compact support, but not yet.

- Discussion Type
- discussion topicdual morphism
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jul 6th 2013

started

*dual morphism*but then began to hesitate: we must have this discussion somewhere already. But where?

- Discussion Type
- discussion topicElementary point-set notion of higher connectedness.
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by TobyBartels
- Last Active Jul 6th 2013

Treating locally path-connected spaces as nice topological spaces, we see that nice path-connected spaces are the same as nice connected spaces, and the definition of the latter is more elementary (in point-set topology) than the former. Then nice simply connected spaces are the same as nice unicoherent spaces, which are again more elementary. This should continue for the entire hierarchy of $n$-connected spaces, so I wrote something there about it.

- Discussion Type
- discussion topicintegration theory - contents
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 5th 2013

started a table of contents

*integration theory - contents*and added it as a floating TOC to the relevant entries.(Mostly as a reminder to myself to write more on fiber integration in generalized cohomology…)

- Discussion Type
- discussion topicfuture of stable homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 5th 2013

Added the following to the references at

*stable homotopy theory*and*algebraic topology*:Brief indications of open questions and future directions (as of 2013) of algebraic topology and stable homotopy theory are in

- Tyler Lawson,
*The future*, Talbot lectures 2013 (pdf)

- Tyler Lawson,

- Discussion Type
- discussion topicasymptotic series
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 5th 2013

created

*asymptotic series*

- Discussion Type
- discussion topicprobability amplitudes
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Urs
- Last Active Jul 4th 2013

Someone started a page called probability amplitudes but with a single word. I have changed that to say the page is empty. (which of course it is not!) as I did not feel competent to write even a stub on that topic.

- Discussion Type
- discussion topicmodels in presheaf toposes
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jul 4th 2013

created

*models in presheaf toposes*with the statement of the fact that T-models in presheaves are presheaves of T-models, at least for T a geometric theory.Added a pointer to this from the corresponding discussion at

*group object*.

- Discussion Type
- discussion topicUniform convergence spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 13
- Last comment by Tim_Porter
- Last Active Jul 3rd 2013

I made a stub uniform convergence space, but I need to read the reference.

- Discussion Type
- discussion topicholographic principle -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 2nd 2013

created a table

*holographic principle – table*(meant to show at on glance what the dictionaty is) and included it into the relevant entries.

- Discussion Type
- discussion topicperfect complex
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jul 2nd 2013

stub for perfect complex

- Discussion Type
- discussion topicKnizhnik-Zamolodchikov connection
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 2nd 2013

I have added to

*Knizhnik-Zamolodchikov connection*a new paragraph in the Idea section:

*Idea – From geometric quantization of Chern-Simons theory*a bunch of commented references

- Discussion Type
- discussion topicAdS/CFT
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by Urs
- Last Active Jul 1st 2013

- Discussion Type
- discussion topicHomotopy groups of connected spaces
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jul 1st 2013

There was some misnumbering (sometimes off by 1, sometimes reversed) at homotopy group#truncconn, which hopefully I've fixed.

- Discussion Type
- discussion topicodd line
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 30th 2013

added to

*odd line*a brief remark on the nature of its automorphism super-group and the consequences, also added some relevant references.(I feel like I had added this statement to the $n$Lab elsewhere already long time ago, but can’t find it now.)

- Discussion Type
- discussion topicgenerator v. separator and Grothendieck category
- Category Latest Changes
- Started by Tim_Porter
- Comments 11
- Last comment by zskoda
- Last Active Jun 25th 2013

I was fixing some Spam at generator and noticed that Grothendieck category has a link to generator, but shouldn’t this be to separator? I have fixed it so that the term generator in Grothendieck category links to separator.

I tried to clear up some formatting problems / typos at separator. (There is a query near the bottom of the page that seems to still be unanswered.) Can someone glance at the entry to check my reformatting is right as I was on autopilot when doing it!

- Discussion Type
- discussion topicThe denial inequality
- Category Latest Changes
- Started by TobyBartels
- Comments 6
- Last comment by Urs
- Last Active Jun 25th 2013

A short note at denial inequality, since the subject came up. Mike, please check that I used ‘disequality’ correctly.

- Discussion Type
- discussion topicLindenbaum-Tarski and Boolean algebras.
- Category Latest Changes
- Started by Tim_Porter
- Comments 14
- Last comment by TobyBartels
- Last Active Jun 25th 2013

Just now I needed a definition and discussion of term algebra for the new entry on Lindenbaum-Tarski algebra. I noted we have Lindenbaum algebra in several places with no explanation. I am no logician and have very few logic books available. Are these the same and what generality should be used for the term algebra.

I also looked at the entry on Boolean algebra and was a bit surprised to find there was no elementary algebraic version given. This is the (for dummies) version perhaps, but seeing one of the usual algebraic description and examples (although these are in the Wikipedia page I’m sure) might enable the ideas about Heyting algebras, lattices, etc., there to be more useful. I’m not sure what level to pitch any additions to that entry, any ideas or thoughts anyone?

- Discussion Type
- discussion topicLogical connectives
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Jun 25th 2013

Just a stub at logical connective.

- Discussion Type
- discussion topicBaer sum
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by Todd_Trimble
- Last Active Jun 24th 2013

I am going to rewrite a part of the Baer sum, the section “On short exact sequences”, partly following S. MacLane,

*Homology*, 1963 (he does the version for extensions of $R$-modules). I am not fully understanding and would like to discuss the issue, but I think the current notation is a bit hiding. So here is the version of the section before my update, so it can be reversed if somebody not happy:For $0 \to A \to \hat G_{i} \to G \to 0$ for $i = 1,2$ two short exact sequences of abelian groups, their

$\hat G_1 + \hat G_2 \coloneqq +_* \Delta^* \hat G_1 \times \hat G_2$**Baer sum**isThe first step forms the pullback of the short exact sequence along rhe diagonal on $G$:

$\array{ A \oplus A &\to& A \oplus A \\ \downarrow && \downarrow \\ \Delta^* (\hat G_1 \oplus \hat G_2) &\to& \hat G_1 \oplus \hat G_2 \\ \downarrow && \downarrow \\ G &\stackrel{\Delta_G}{\to}& G\oplus G }$The second forms the pushout along the addition map on $A$:

$\array{ A \oplus A &\stackrel{+}{\to}& A \\ \downarrow && \downarrow \\ \Delta^* (\hat G_1 \oplus \hat G_2) &\to& +_* \Delta^*(\hat G_1 \oplus \hat G_2) \\ \downarrow && \downarrow \\ G &\to& G }$

- Discussion Type
- discussion topicRelative Postnikov tower
- Category Latest Changes
- Started by MatanP
- Comments 1
- Last comment by MatanP
- Last Active Jun 24th 2013

I’ve changed Postnikov system definition 2

the part saying

“The map $X \to im_n(f)$ induces an epimorphism on connected components”

to

“The map $X \to im_n(f)$ induces an epimorphism on homotopy groups in degree $n-1$”.

This was a small issue that confused me.

- Discussion Type
- discussion topicaxiom K
- Category Latest Changes
- Started by Tim_Porter
- Comments 5
- Last comment by TobyBartels
- Last Active Jun 22nd 2013

There is a query at axiom K.

- Discussion Type
- discussion topicQuest for Unification
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 21st 2013

added a pointer to the old lecture

- Edward Witten,
*Quest For Unification*, Heinrich Hertz lecture at SUSY 2002 at DESY, Hamburg (arXiv:hep-ph/0207124)

to

*GUT*and*string phenomenology*.- Edward Witten,

- Discussion Type
- discussion topicextensional and intensional type theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Mike Shulman
- Last Active Jun 21st 2013

earlier today I had started splitting off entries intensional type theory and extensional type theory from type theory. But then the Lab halted and now it’s left in somewhat stubby form.

- Discussion Type
- discussion topicLimit points
- Category Latest Changes
- Started by TobyBartels
- Comments 12
- Last comment by TobyBartels
- Last Active Jun 21st 2013

I've seen two meanings for this term, and they are both at limit point, along with a family of other terms for various arity classes.

- Discussion Type
- discussion topicConvergence
- Category Latest Changes
- Started by TobyBartels
- Comments 6
- Last comment by TobyBartels
- Last Active Jun 21st 2013

Urs created limit of a sequence on this topic.