Relative singular value decomposition and applications to LS-category

Abstract

Let Sp(n) be the symplectic group of quaternionic (n × n)-matrices. For any 1 ≤ k ≤ n, an element A of Sp(n)In this work, starting from a singular value decomposition of P , we obtain what we call a relative singular value decomposition of A. This feature is well adapted for the study of the quaternionic Stiefel manifold X n,k , and we apply it to the determination of the Lusternik-Schnirelmann category of Sp(k) in X 2k−j,k , for j = 0, 1, 2.2010 Mathematics Subject Classification. Primary 15A33; Secondary 22E20, 22F30, 55M30.