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Locally linear actions on 3-manifolds

Published online by Cambridge University Press:  24 October 2008

SŁawomir Kwasik  and
Kyung Bai Lee
SŁawomir Kwasik
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A.
Kyung Bai Lee
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A.
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Extract

Let a finite group G act topologically on a closed smooth manifold Mn. One of the most natural and basic questions is whether such an action can be smoothed. More precisely, let γ:G × Mn → Mn be a topological action of G on Mn. The action γ can be smoothed if there exists a smooth action and an equivariant homeomorphism It is well known that for n ≤ 2 every finite topological group action on Mn is smoothable. However already for n = 3 there are examples of topological actions on 3-manifolds which cannot be smoothed (see [1, 2] and references there). All these actions fail to be smoothable because of bad local behaviour.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 253 - 260
Copyright
Copyright © Cambridge Philosophical Society 1988

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