Finite groups with smooth one fixed point actions on spheres

Erkki Laitinen; Masaharu Morimoto

doi:10.1515/form.10.4.479

Finite groups with smooth one fixed point actions on spheres

Erkki Laitinen, Masaharu Morimoto

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

Since 1946 it has been an open question which compact Lie groups can act smoothly on some sphere with exactly one fixed point. In this paper we solve the problem completely for finite groups: these groups are exactly those which can act smoothly on some disk without fixed points, a class determined by R. Oliver. Our main tools are the Burnside ring and the Grothendieck-Witt ring (classical to some extent) and a form of equivariant surgery theory allowing middle-dimensional singular sets developed recently.

Original language	English
Pages (from-to)	479-520
Number of pages	42
Journal	Forum Mathematicum
Volume	10
Issue number	4
DOIs	https://doi.org/10.1515/form.10.4.479
Publication status	Published - Jan 1 1998

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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Finite groups with smooth one fixed point actions on spheres

Abstract

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