Deleting-Inserting Theorem for smooth actions of finite nonsolvable groups on spheres

Erkki Laitinen, Masaharu Morimoto, Krzysztof Pawalowski

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The paper presents a method which allows to construct smooth finite nonsolvable group actions on spheres with prescribed fixed point data. The idea is to consider an action on a disk with the required fixed point data, and then to apply equivariant surgery to the equivariant double of the disk to remove the second copy of the fixed point data. In this paper, the method is applied to construct smooth group actions on spheres with exactly one fixed point, and more general actions with fixed point set diffeomorphic to any given closed stably parallelizable smooth manifold. The method is expected to be useful for constructions of smooth group actions on spheres with more complicated fixed point data.

Original languageEnglish
Pages (from-to)10-38
Number of pages29
JournalCommentarii Mathematici Helvetici
Volume70
Issue number1
DOIs
Publication statusPublished - Dec 1995

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Finite Group
Fixed point
Theorem
Group Action
Equivariant
Finite Group Action
Fixed Point Set
Smooth Manifold
Surgery
Closed

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Deleting-Inserting Theorem for smooth actions of finite nonsolvable groups on spheres. / Laitinen, Erkki; Morimoto, Masaharu; Pawalowski, Krzysztof.

In: Commentarii Mathematici Helvetici, Vol. 70, No. 1, 12.1995, p. 10-38.

Research output: Contribution to journalArticle

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