Quantum invariants and finite group actions on three-manifolds

2003/10/29 by Nafaa Chbili, Chbili, Nafaa
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0310459

16 pages 4 figures

arxiv created 2003/10/29 · arxiv updated 2009/12/01

Abstract

A 3-manifold M is said to be p-periodic (p≥ 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.

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