### Abstract

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.

Original language | English |
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Pages (from-to) | 1003-1013 |

Number of pages | 11 |

Journal | Osaka Journal of Mathematics |

Volume | 53 |

Issue number | 4 |

Publication status | Published - Oct 1 2016 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Osaka Journal of Mathematics*,

*53*(4), 1003-1013.

**One-fixed-point actions on spheres and smith sets.** / Morimoto, Masaharu.

Research output: Contribution to journal › Article

*Osaka Journal of Mathematics*, vol. 53, no. 4, pp. 1003-1013.

}

TY - JOUR

T1 - One-fixed-point actions on spheres and smith sets

AU - Morimoto, Masaharu

PY - 2016/10/1

Y1 - 2016/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990045957&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990045957&partnerID=8YFLogxK

M3 - Article

VL - 53

SP - 1003

EP - 1013

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 4

ER -