Volume 7, issue 4 (2007)

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Period three actions on lens spaces

Joseph Maher

Algebraic & Geometric Topology 7 (2007) 2021–2102
 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