Finite groups acting on hyperelliptic 3-manifolds

Mattia Mecchia

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arXiv · 1805.06331

Finite groups acting on hyperelliptic 3-manifolds

Mattia Mecchia

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Abstract

We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to $S^3.$ Such involutions are called hyperelliptic as the manifolds admitting such an action. We consider finite groups acting on 3-manifolds and containing hyperelliptic involutions whose fixed-point set has $r>2$ components. In particular we prove that a simple group containing such an involution is isomorphic to $PSL(2,q)$ for some odd prime power $q$, or to one of four other small simple groups.

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BibTeX RIS

Mattia Mecchia. 2018-05-16. Finite groups acting on hyperelliptic 3-manifolds. https://arxiv.org/abs/1805.06331

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