Quantum invariants and finite group actions on three-manifolds

Abstract

A 3-manifold $M$ is said to be $p$-periodic ($p\ge 2$ an integer) if and only if the finite cyclic group of order $p$ acts on $M$ with a circle as the set of fixed points. This paper provides a criterion for periodicity of rational homology three-spheres. Namely, we give a necessary condition for a rational homology three-sphere to be periodic with a prime period. This condition is given in terms of the quantum SU(3) invariant. We also discuss similar results for the Murakami-Ohtsuki-Okada invariant.

16 pages 4 figures

References in corpus (1)

• Quantum Invariants of Periodic Links and Periodic 3-Manifolds