Equivariant surgery theory

Deleting-inserting theorems of fixed point manifolds on spheres and disks

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The paper gives a tool to delete and insert fixed point manifolds for smooth actions of finite Oliver groups on spheres and disks. A similar result was already given in a joint article with E. Laitinen and K. Pawalowski for those of finite nonsolvable groups on spheres. It is useful in classifying smooth actions on spheres from the view point of fixed point data. The methods employed in the present paper are equivariant surgery and equivariant connected sum associated with elements in the Burnside ring. The idea of killing surgery obstructions is as follows: Let G be a finite group not of prime power order, C a contractible, finite G-CW complex, and σ an element in a K-theoretic group arising as an obstruction class of geometric object f. It often holds that (1 - [C])mσ becomes trivial for large integers m, where [C] is the element represented by C in the Burnside ring Ω(G). One expects that the algebraic object (1 - [C])mσ is realizable as the obstruction class of G-connected sum of f's related to (1 - [C])m. Since it is true for the case here, we can kill the obstruction σ by taking G-connected sum of f's.

Original languageEnglish
Pages (from-to)13-32
Number of pages20
JournalK-Theory
Volume15
Issue number1
Publication statusPublished - 1998

Fingerprint

Obstruction
Equivariant
Connected Sum
Surgery
Fixed point
Burnside Ring
Theorem
Finite Group
Algebraic object
CW-complex
Geometric object
Trivial
Integer
Class

Keywords

  • Equivariant surgery
  • Fixed point
  • Smooth action

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Equivariant surgery theory : Deleting-inserting theorems of fixed point manifolds on spheres and disks. / Morimoto, Masaharu.

In: K-Theory, Vol. 15, No. 1, 1998, p. 13-32.

Research output: Contribution to journalArticle

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