Finite groups with smooth one fixed point actions on spheres

Erkki Laitinen, Masaharu Morimoto

Research output: Contribution to journalArticle

28 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 languageEnglish
Pages (from-to)479-520
Number of pages42
JournalForum Mathematicum
Volume10
Issue number4
Publication statusPublished - 1998

Fingerprint

Lie groups
Surgery
Finite Group
Fixed point
Burnside Ring
Witt Ring
Singular Set
Compact Lie Group
Equivariant
Form
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Finite groups with smooth one fixed point actions on spheres. / Laitinen, Erkki; Morimoto, Masaharu.

In: Forum Mathematicum, Vol. 10, No. 4, 1998, p. 479-520.

Research output: Contribution to journalArticle

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