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

Christian Blanchet (1) , Francesco Costantino (2) , Nathan Geer , Bertrand Patureau-Mirand (3)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

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.

Domaines: Topologie géométrique [math.GT]

Christian Blanchet, Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand. Non semi-simple TQFTs from unrolled quantum $sl(2)$. Journal of Gökova Geometry Topology, 2015, Gökova Geometry/Topology Conference (GGT) 2015. ⟨hal-01328737⟩