Finite groups acting on hyperelliptic 3-manifolds
- Resource Type
- Working Paper
- Authors
- Mecchia, Mattia
- Source
- Subject
- Mathematics - Geometric Topology
57M60, 57M12, 57M25
- Language
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.
Comment: 13 pages