Fixed-point sets of smooth actions on spheres

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Given a group, it is a basic problem to determine which manifolds can occur as a fixed-point set of a smooth action of this group on a sphere. The current article answers this problem for a family of finite groups including perfect groups and nilpotent Oliver groups. We obtain the answer as an application of a new deleting and inserting theorem which is formulated to delete (or insert) fixed-point sets from (or to) disks with smooth actions of finite groups. One of the keys to the proof is an equivariant interpretation of the surgery theory of S. E. Cappell and J. L. Shaneson, for obtaining homology equivalences.

Original languageEnglish
Pages (from-to)95-128
Number of pages34
JournalJournal of K-Theory
Volume1
Issue number1
DOIs
Publication statusPublished - 2008

Keywords

  • Equivariant surgery
  • fixed point
  • sphere
  • strong gap condition
  • surgery obstruction

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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