Quantum invariants and finite group actions on three-manifolds

Details Quantum invariants and finite group actions on three-manifolds Quantum invariants and finite group actions on three-manifolds

2003-10-29

arxiv.org/abs/math/0310459v1

Mathematics

Geometric Topology

16 pages 4 figures

Scientific paper

A 3-manifold $M$ is said to be $p$-periodic ($p\geq 2$ 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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