Bounding finite groups acting on 3-manifolds
- 1 September 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 96 (2) , 269-281
- https://doi.org/10.1017/s0305004100062162
Abstract
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.Keywords
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