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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 15th 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAccording to this [MO question]( http://mathoverflow.net/questions/163301/what-is-chern-simons-theory-expected-to-assign-to-a-point) -- What is Chern-Simons theory expected to assign to a point? -- >The nLab is somewhat vague on this subject I wonder if this concerns [[Topological Quantum Field Theories from Compact Lie Groups]] or some other page.

   According to this MO question – What is Chern-Simons theory expected to assign to a point? –

   The nLab is somewhat vague on this subject

   I wonder if this concerns Topological Quantum Field Theories from Compact Lie Groups or some other page.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeApr 15th 2014
   • (edited Apr 15th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexYeah, I saw this comment, too. Made me laugh; this is a bit like: "Is $P \neq NP$? The $n$Lab is a bit vague about this point." Anyway, giving a full description of 3d Chern-Simons as a fully extended TQFT is one of the big open questions, of which however a great deal is "in the air". Depending on how you squint your eyes, it's known or not. Teleman et al have been giving talks about this for a while now, one of which the above notes were taken in. Of course eventually we should have plenty more discussion of all this on the $n$Lab. Strangely, the entries don't write themselves. I'll close with just one comment: by what we have been discussing elsewhere, the quantization is naturally expected to be $tmf$-linear and be based on the $G$-equivariant $tmf$-cohomology (push of $\mathbf{B}G \to \mathbf{B}^3 U(1) \to \mathbf{B}GL_1(tmf) $), hence $G$-equivariant elliptic cohomology. That [subsumes](http://ncatlab.org/nlab/show/equivariant%20elliptic%20cohomology#RelationToLoopGroupRepresentations) the loop group representations that André is proposing to assign to the point.

   Yeah, I saw this comment, too. Made me laugh; this is a bit like: “Is $P \neq NP$? The $n$Lab is a bit vague about this point.”

   Anyway, giving a full description of 3d Chern-Simons as a fully extended TQFT is one of the big open questions, of which however a great deal is “in the air”. Depending on how you squint your eyes, it’s known or not. Teleman et al have been giving talks about this for a while now, one of which the above notes were taken in.

   Of course eventually we should have plenty more discussion of all this on the $n$Lab. Strangely, the entries don’t write themselves.

   I’ll close with just one comment: by what we have been discussing elsewhere, the quantization is naturally expected to be $tmf$-linear and be based on the $G$-equivariant $tmf$-cohomology (push of $\mathbf{B}G \to \mathbf{B}^3 U(1) \to \mathbf{B}GL_1(tmf)$), hence $G$-equivariant elliptic cohomology. That subsumes the loop group representations that André is proposing to assign to the point.