Bott periodicity for inclusions of symmetric spaces
Augustin-Liviu Mare
Department of Mathematics Institut für Mathematik and Statistics Universität Augsburg University of Regina Germany CanadaPeter Quast
Department of Mathematics Institut für Mathematik and Statistics Universität Augsburg University of Regina Germany Canada
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