One-fixed-point actions on spheres and smith sets

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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 languageEnglish
Pages (from-to)1003-1013
Number of pages11
JournalOsaka Journal of Mathematics
Issue number4
Publication statusPublished - Oct 1 2016


ASJC Scopus subject areas

  • Mathematics(all)

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