# Non-Semisimple Quantum Invariants and TQFTs from Small and Unrolled Quantum Goups

## TL;DR

This paper constructs non-semisimple quantum invariants and TQFTs from unrolled quantum groups at odd roots of unity, extending CGP invariants to a broader class of 3-manifold invariants.

## Contribution

It introduces relative modular categories from unrolled quantum groups, enabling the construction of 1+1+1-TQFTs that extend existing quantum invariants.

## Key findings

- Unrolled quantum groups at odd roots of unity form relative modular categories.
- Constructed 1+1+1-TQFTs extending CGP invariants.
- Quantum invariants coincide with renormalized Hennings invariants at zero cohomology.

## 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 1+1+1-TQFTs extending CGP invariants, which are non-semisimple 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.