Timeline for Principal $G$-bundles as fully extended TQFTs, and $n$-representations
Current License: CC BY-SA 3.0
12 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 13, 2012 at 18:58 | history | edited | Dmitri Pavlov | CC BY-SA 3.0 |
deleted 2 characters in body
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| Mar 13, 2012 at 18:58 | comment | added | Dmitri Pavlov | The name is Teleman, not Telemann. | |
| Jul 2, 2011 at 16:34 | comment | added | domenico fiorenza | Hi David, thanks for the remark. But then this means that $*//G$ is a homotopy fixed point for the action of $SO(n)$ on $Fam_n$, doesn't it? And since you teach me the homotopy fixed structure is not unique in general, this means the one leading to $Bun_G$ is just a distinguished one (trivial one?); what do the other structures correspond to? ("twisted" $G$-bundles?) | |
| Jul 2, 2011 at 14:48 | comment | added | David Ben-Zvi | The cobordism hypothesis has a slightly different form for oriented bordisms -- i.e., you need not just a fully dualizable object but one equipped with a homotopy fixed structure for $SO_n$, which is not uniquely specified (if it exists) by the object. | |
| Jul 1, 2011 at 16:18 | history | edited | domenico fiorenza | CC BY-SA 3.0 |
point ii) better specified
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| Jul 1, 2011 at 16:16 | comment | added | domenico fiorenza | "determined by $G$" there stands for $F(pt^+)=*//G$, which is the form I'm using a few lines above. I'm now editing the question to specify this. | |
| Jul 1, 2011 at 7:25 | comment | added | S. Carnahan♦ | I am having trouble extracting a precise statement from conclusion ii. In particular, "determined by G" does not seem to be a precisely formulated condition. | |
| Jun 30, 2011 at 18:10 | comment | added | domenico fiorenza | Hi Theo, thanks a lot for your comments. You perfectly read my question: it is a twofold question: i) does the one-line summary of FHLT says that a classical field theory is a representation $G\to$ some delooping of Vect? (seems so, but such a bold statement is not explicitly in FHLT) ii) are there in the algebra/representation theory literaure examples of representation $G\to$ some delooping of Vect not discussed in the examples of FHLT? if so, are the associated TQFT identified with known TQFTs? | |
| Jun 30, 2011 at 14:40 | comment | added | Theo Johnson-Freyd | By "other examples", I take you to mean the following: FHLT translate between some homological data and representations $G \to $ some delooping of Vect. You are asking if this is all the basic representations? Or maybe I misunderstand you and/or FHLT. | |
| Jun 30, 2011 at 14:34 | comment | added | Theo Johnson-Freyd | For readers who have not recently read FHTL, I recall that $Fam_n$ is the $(\infty,n)$-category whose objects are finite groupoids, 1-morphisms are correspondences of finite groupoids, 2-morphisms are correspondences of correspondences, and so on up to n-morphisms; the (n+1)-morphisms and higher are equivalences. The "SO" on $Bord^{SO}_n$ reminds the reader that this is the category of n-framed bordisms. | |
| Jun 30, 2011 at 11:09 | history | asked | domenico fiorenza | CC BY-SA 3.0 |