Period three actions on lens spaces

Maher, Joseph

doi:10.2140/agt.2007.7.2021

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Period three actions on lens spaces

Joseph Maher

Algebraic & Geometric Topology 7 (2007) 2021–2102

DOI: 10.2140/agt.2007.7.2021

arXiv: math.GT/0311009

Abstract

We prove that a free $ℤ_{3}$ action on a lens space is standard. This extends to lens spaces earlier work of Maher and Rubinstein on $ℤ_{3}$ actions on $S^{3}$ . It follows using previously known results that a free action of a group of order $2^{a} 3^{b}$ on $S^{3}$ is standard.

Keywords

3–manifold, 3–sphere, lens space, $\mathbb{Z}_3$–action, group action, spherical 3–manifold

Mathematical Subject Classification 2000

Primary: 57N10, 57M50, 57M60

Secondary: 57M40

References

Publication

Received: 4 November 2003

Revised: 25 September 2007

Accepted: 24 October 2007

Published: 26 December 2007

Authors

Joseph Maher
Department of Mathematics Oklahoma State University 427 Mathematical Sciences Stillwater OK 74078 USA
http://www.math.okstate.edu/~maher/

Volume 7, issue 4 (2007)