Non semi-simple TQFTs from unrolled quantum $sl(2)$

Abstract

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum $sl(2)$ were obtained by the last three authors in arXiv:1202.3553 . They are invariants of $3$-manifolds together with a cohomology class which can be interpreted as a line bundle with flat connection. In arXiv:1404.7289 we have extended those invariants to graded TQFTs on suitable cobordism categories. Here we give an overview of constructions and results, and describe the TQFT vector spaces. Then we provide a new, algebraic, approach to the computation of these vector spaces.

Proceedings of the Gokova Geometry-Topology Conference 2015, International Press of Boston, Inc. (May 2016)

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