Vol. 66, No. 1, 1976

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Local S1 actions on 3-manifolds

Ronald Fintushel

Vol. 66 (1976), No. 1, 111–118

A classification is given for S1 bundles with structure group O(2) and base space a 2-manifold with nonempty boundary. This result is used to obtain equivariant and topological classification theorems for closed 3-manifolds which admit a local S1 action; i.e., a decomposition into circles and points such that each decomposition element has an invariant neighborhood admitting an effective circle action with the elements of the decomposition as orbits. This extends certain results of Orlik and Raymond and corrects a theorem of Orlik, Vogt, and Zieschang.

Mathematical Subject Classification
Primary: 57E25, 57E25
Received: 11 July 1975
Published: 1 September 1976
Ronald Fintushel
Department of Mathematics
Michigan State University
Wells Hall
East Lansing MI 48824-1027
United States