Topological classification of multiaxial U(n)-actions

Sylvain Cappell, Shmuel Weinberger, Min Yan, Jared Bass

Research output: Contribution to journalArticle

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

Fingerprint

Lie groups
Schubert Calculus
Analytic group
Symplectic Group
Grassmannian
Unitary group
Differentiable
Circle
Restriction
Standards

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Topological classification of multiaxial U(n)-actions. / Cappell, Sylvain; Weinberger, Shmuel; Yan, Min; Bass, Jared.

In: Journal of the European Mathematical Society, Vol. 17, No. 9, 2015, p. 2175-2208.

Research output: Contribution to journalArticle

Cappell, S, Weinberger, S, Yan, M & Bass, J 2015, 'Topological classification of multiaxial U(n)-actions', Journal of the European Mathematical Society, vol. 17, no. 9, pp. 2175-2208. https://doi.org/10.4171/JEMS/554
Cappell, Sylvain ; Weinberger, Shmuel ; Yan, Min ; Bass, Jared. / Topological classification of multiaxial U(n)-actions. In: Journal of the European Mathematical Society. 2015 ; Vol. 17, No. 9. pp. 2175-2208.
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