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Finite group actions on homologically peripheral 3-manifolds

Published online by Cambridge University Press:  10 June 2011

TORU IKEDA
TORU IKEDA*
Affiliation:
Department of Mathematics, Faculty of Science, Kochi University, 2-5-1 Akebono-cho, Kochi 780-8520, Japan. e-mail: ikedat@kochi-u.ac.jp
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Abstract

We generalize the notion of totally peripheral 3-manifolds to define homologically peripheral 3-manifolds. The homologically peripheral property survives canonical decompositions of 3-manifolds as well as it defines a sufficiently large class of 3-manifolds containing link exteriors. The aim of this paper is to study finite group actions on a homologically peripheral 3-manifold, which agree on the boundary, up to equivalence relative to the boundary. As an application, we generalize Sakuma's theorems on the uniqueness of symmetries of knots to the case of symmetries of links.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 2 , September 2011 , pp. 319 - 337
Copyright
Copyright © Cambridge Philosophical Society 2011

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