Physics Group Meeting

I would like to discuss the problem of categorification of Chern-Simons partition function on closed 3-manifolds. Physics constructions of Khovanov knot homology, which categorifies Jones polynomial, suggests that there should be a generalization to the case of arbitrary closed 3-manifolds. Part of the problem is rewriting Chern-Simons partition function in terms of q-series with integer coefficients, where q is the same variable that appears in Jones polynomial.

References:

1) Some recent progress in the direction:

http://arxiv.org/abs/arXiv:1602.05302 (sec. 6)

2) Physics interpretation of Khovanov homology of knots:

http://arxiv.org/abs/hep-th/0412243
http://arxiv.org/abs/arXiv:1101.3216

3) Relation of Chern-Simons partition function on certain Seifert 3-manifolds to mock modular forms:

http://people.mpim-bonn.mpg.de/zagier/files/ajm/3-1/fulltext.pdf

4) Analytic continuation of CS:

http://arxiv.org/abs/arXiv:1001.2933