Period three actions on the three-sphere

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

References

Forward citations

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

Volume 7, issue 1 (2003)

Joseph Maher and J Hyam Rubinstein