Volume 7, issue 1 (2003)

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Period three actions on the three-sphere

Joseph Maher and J Hyam Rubinstein

Geometry & Topology 7 (2003) 329–397

arXiv: math.GT/0204077

Abstract

We show that a free period three action on the three-sphere is standard, ie, the quotient is homeomorphic to a lens space. We use a minimax argument involving sweepouts.

Keywords
3–manifold, 3–sphere, group action, spherical 3–manifold, lens space
Mathematical Subject Classification 2000
Primary: 57M60
Secondary: 57M50
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Publication
Received: 6 April 2002
Revised: 1 June 2003
Accepted: 23 May 2003
Published: 19 June 2003
Proposed: Cameron Gordon
Seconded: Walter Neumann, Joan Birman
Authors
Joseph Maher
Mathematics 253-37
California Institute of Technology
Pasadena
California 91125
USA
J Hyam Rubinstein
Department of Mathematics and Statistics
University of Melbourne
Parkville
Victoria 3010
Australia