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Bounding finite groups acting on 3-manifolds

Published online by Cambridge University Press:  24 October 2008

Sadayoshi Kojima
Sadayoshi Kojima
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Japan
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Extract

In Problem 3·39 (B) and (C) of Kirby's collection [10], Giffen and Thurston asked whether, for a closed 3-manifold M, the order of finite subgroups of Diff M is bounded, so that it contains no infinite torsion subgroups unless M admits a circle action. In this paper, we answer this question affirmatively for homotopy geometric manifolds, and then discuss some hyperbolic 3-manifolds with only a few actions as examples showing poor symmetry of 3-manifolds in general.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 2 , September 1984 , pp. 269 - 281
Copyright
Copyright © Cambridge Philosophical Society 1984

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