Quantum invariants of 3-manifolds associated to restricted quantum groups

TL;DR

This paper demonstrates that the Witten-Reshetikhin-Turaev SU(2) invariant and the Hennings invariant, both quantum invariants of 3-manifolds, coincide for rational homology 3-spheres, linking two important quantum invariants.

Contribution

It establishes the equivalence of two prominent quantum invariants for a class of 3-manifolds, providing new insights into their relationship.

Findings

Witten-Reshetikhin-Turaev SU(2) invariant and Hennings invariant are essentially the same for rational homology 3-spheres.

The result bridges different approaches to quantum invariants of 3-manifolds.

The paper clarifies the connection between invariants derived from restricted quantum groups and topological quantum field theories.

Abstract

We show that the Witten-Reshetikhin-Turaev SU(2) invariant and the Hennings invariant associated to the restricted quantum $sl_2$ are essentially the same for rational homology 3-spheres.