#### Volume 20, issue 7 (2020)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Nonsemisimple quantum invariants and TQFTs from small and unrolled quantum groups

### Marco De Renzi, Nathan Geer and Bertrand Patureau-Mirand

Algebraic & Geometric Topology 20 (2020) 3377–3422
##### Abstract

We show that unrolled quantum groups at odd roots of unity give rise to relative modular categories. These are the main building blocks for the construction of $\left(1+1+1\right)$–TQFTs extending CGP invariants, which are nonsemisimple quantum invariants of closed $3$–manifolds decorated with ribbon graphs and cohomology classes. When we consider the zero cohomology class, these quantum invariants are shown to coincide with the renormalized Hennings invariants coming from the corresponding small quantum groups.

##### Keywords
nonsemisimple quantum invariants, nonsemisimple TQFTs, small quantum groups, unrolled quantum groups
##### Mathematical Subject Classification 2010
Primary: 57M27, 81R50