The Equivariant Bundle Subtraction Theorem and its applications

Masaharu Morimoto, Krzysztof Pawałowski

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In the theory of transformation groups, it is important to know what kind of isotropy subgroups of G do occur at points of the space upon which the given group G acts. In this article, for a finite group G, we prove the Equivariant Bundle Subtraction Theorem (Theorem 2.2) which allows us to construct smooth G-manifolds with prescribed isotropy subgroups around the G-fixed point sets. In Theorem 0.1, we restate Oliver's result about manifolds M and G-vector bundles over M that occur, respectively, as the G-fixed point sets and their equivariant normal bundles for smooth G-actions on disks. In Theorems 0.2 and 0.3, we prove the corresponding results for smooth G-actions on disks with prescribed isotropy subgroups around M. In Theorems 0.4 and 0.5, for large classes of finite groups G, we explicitly describe manifolds M that occur as the G-fixed point sets for such actions on disks. These actions are expected to be useful for answering the question of which manifolds occur as the G-fixed points sets for smooth G-actions on spheres.

Original languageEnglish
Pages (from-to)279-303
Number of pages25
JournalFundamenta Mathematicae
Volume161
Issue number3
Publication statusPublished - Dec 1 2000

Keywords

  • Equivariant bundle subtraction
  • Equivariant normal bundle
  • Fixed point set
  • Smooth action on disk
  • The family of large subgroups of a finite group

ASJC Scopus subject areas

  • Algebra and Number Theory

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  • Cite this

    Morimoto, M., & Pawałowski, K. (2000). The Equivariant Bundle Subtraction Theorem and its applications. Fundamenta Mathematicae, 161(3), 279-303.