Quantum invariants and free Z_{p^2} -actions on 3-manifolds

TL;DR

This paper establishes a congruence relation for quantum invariants of 3-manifolds with Z_{p^2} actions, highlighting its limitations for certain group actions like Z_{5}xZ_{5}.

Contribution

It introduces a new congruence formula for quantum invariants under Z_{p^2} actions on 3-manifolds and identifies cases where it does not apply.

Findings

Congruence holds for Z_p-quotients with Z_{p^2} actions.

The congruence fails for quotients with Z_{5}xZ_{5} actions.

Provides insight into quantum invariants under specific group actions.

Abstract

We give a congruence for the quantum invariant of a Z_p-quotient of a 3$-manifold with a Z_{p^2} action. We show the congruence does not hold for quotients of 3--manifolds with a Z_{5}xZ_{5} action.