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

Understand

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.