JournalsjemsVol. 17, No. 9pp. 2175–2208

Topological classification of multiaxial U(n)U(n)-actions (with an appendix by Jared Bass)

  • Sylvain Cappell

    New York University, USA
  • Shmuel Weinberger

    University of Chicago, United States
  • Min Yan

    Hong Kong University of Science and Technology, China
Topological classification of multiaxial $U(n)$-actions (with an appendix by Jared Bass) cover
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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.

Cite this article

Sylvain Cappell, Shmuel Weinberger, Min Yan, Topological classification of multiaxial U(n)U(n)-actions (with an appendix by Jared Bass). J. Eur. Math. Soc. 17 (2015), no. 9, pp. 2175–2208

DOI 10.4171/JEMS/554