Bott periodicity for inclusions of symmetric spaces

  • Augustin-Liviu Mare

    Department of Mathematics and Statistics, University of Regina, Canada
  • Peter Quast

    Institut für Mathematik, Universität Augsburg, Germany
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Abstract

When looking at Bott's original proof of his periodicity theorem for the stable homotopy groups of the orthogonal and unitary groups, one sees in the background a differential geometric periodicity phenomenon. We show that this geometric phenomenon extends to the standard inclusion of the orthogonal group into the unitary group. Standard inclusions between other classical Riemannian symmetric spaces are considered as well. An application to homotopy theory is also discussed.

Cite this article

Augustin-Liviu Mare, Peter Quast, Bott periodicity for inclusions of symmetric spaces. Doc. Math. 17 (2012), pp. 911–952

DOI 10.4171/DM/385