Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 53, Number 4 (2016), 1003-1013.
One-fixed-point actions on spheres and Smith sets
Let $G$ be a finite group. The Smith equivalence for real $G$-modules of finite dimension gives a subset of real representation ring, called the primary Smith set. Since the primary Smith set is not additively closed in general, it is an interesting problem to find a subset which is additively closed in the real representation ring and occupies a large portion of the primary Smith set. In this paper we introduce an additively closed subset of the primary Smith set by means of smooth one-fixed-point $G$-actions on spheres, and we give evidences that the subset occupies a large portion of the primary Smith set if $G$ is an Oliver group.
Osaka J. Math., Volume 53, Number 4 (2016), 1003-1013.
First available in Project Euclid: 4 October 2016
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Morimoto, Masaharu. One-fixed-point actions on spheres and Smith sets. Osaka J. Math. 53 (2016), no. 4, 1003--1013. https://projecteuclid.org/euclid.ojm/1475601828