Topological classification of multiaxial U(n)-actions

Sylvain Cappell, Shmuel Weinberger, Min Yan, Jared Bass

Research output: Contribution to journalArticlepeer-review

Abstract

This paper begins the classification of topological actions on manifolds by compact, connected, Lie groups beyond the circle group. It treats multiaxial topological actions of unitary and symplectic groups without the dimension restrictions used in earlier works by M. Davis and W. C. Hsiang on differentiable actions. The general results are applied to give detailed calculations for topological actions homotopically modeled on standard multiaxial representation spheres. In the present topological setting, Schubert calculus of complex Grassmannians surprisingly enters in the calculations, yielding a profusion of "fake" representation spheres compared with the paucity in the previously studied smooth setting.

Original languageEnglish (US)
Pages (from-to)2175-2208
Number of pages34
JournalJournal of the European Mathematical Society
Volume17
Issue number9
DOIs
StatePublished - 2015

Keywords

  • Assembly map
  • Multiaxial
  • Stratified space
  • Surgery
  • Topological manifold
  • Transformation group

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Topological classification of multiaxial U(n)-actions'. Together they form a unique fingerprint.

Cite this