Osaka Journal of Mathematics

Spheres not admitting smooth odd-fixed-point actions of $S_5$ and $SL(2, 5)$

Masaharu Morimoto and Shunsuke Tamura

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Let $G$ be a finite group and $\Sigma$ a homology sphere with smooth $G$-action. If the $G$-fixed-point set of $\Sigma$ consists of odd-number points then the dimension of $\Sigma$ could be restrictive. In this article we confirm the claim in the cases where $G = S_5$ or $S\!L(2, 5)$.

Article information

Osaka J. Math., Volume 57, Number 1 (2020), 1-8.

First available in Project Euclid: 15 January 2020

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Mathematical Reviews number (MathSciNet)

Primary: 57S25: Groups acting on specific manifolds
Secondary: 55M35: Finite groups of transformations (including Smith theory) [See also 57S17]


Morimoto, Masaharu; Tamura, Shunsuke. Spheres not admitting smooth odd-fixed-point actions of $S_5$ and $SL(2, 5)$. Osaka J. Math. 57 (2020), no. 1, 1--8.

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