Local S¹ actions on 3-manifolds

Ronald Fintushel

Vol. 66 (1976), No. 1, 111–118

DOI: 10.2140/pjm.1976.66.111

Abstract

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

Milestones

Received: 11 July 1975

Published: 1 September 1976