Geometry & Topology, Vol. 7 (2003) Paper no. 11, pages 329--397.

Period three actions on the three-sphere

Joseph Maher, J Hyam Rubinstein

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

AMS subject classification. Primary: 57M60. Secondary: 57M50.

DOI: 10.2140/gt.2003.7.329

E-print: arXiv:math.GT/0204077

Submitted to GT on 6 April 2002. (Revised 1 June 2003.) Paper accepted 23 May 2003. Paper published19 June 2003.

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Joseph Maher, J Hyam Rubinstein
Mathematics 253-37, California Institute of Technology
Pasadena, CA 91125, USA
and
Department of Mathematics and Statistics
University of Melbourne, Parkville VIC 3010, Australia

Email: maher@its.caltech.edu, rubin@ms.unimelb.edu.au

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