Smooth actions of finite Oliver groups on spheres

Masaharu Morimoto, Krzysztof Pawałowski

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this article, we deal with the following two questions. For smooth actions of a given finite group G on spheres S, which smooth manifolds F occur as the fixed point sets in S, and which real G-vector bundles ν over F occur as the equivariant normal bundles of F in S? We focus on the case G is an Oliver group and answer both questions under some conditions imposed on G, F, and ν. We construct smooth actions of G on spheres by making use of equivariant surgery, equivariant thickening, and Oliver's equivariant bundle extension method modified by an equivariant wegde sum construction and an equivariant bundle subtraction procedure.

Original languageEnglish
Pages (from-to)395-421
Number of pages27
JournalTopology
Volume42
Issue number2
DOIs
Publication statusPublished - Mar 2003

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Keywords

  • Equivariant bundle extension
  • Equivariant bundle subtraction
  • Equivariant normal bundle
  • Equivariant surgery
  • Equivariant thickening
  • Fixed point set
  • Gap group
  • Oliver group
  • Oliver obstruction
  • Smooth action on sphere

ASJC Scopus subject areas

  • Geometry and Topology

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