L'interpretation de la classe de Maslov dans la K-theorie Hermitienne et dans la theorie relative de Chern-Weil

Abstract

The purpose of this paper is, first to define the Maslov invariant in the U-theory, the intermediate theory between real K-theory and complex K-theory, whose vanishing is a necessary and sufficient condition for the stable transversality of two Lagrangian sub-bundles of a symplectic fiber bundle. The second purpose is to show, in conformity with Bott periodicity, that Chern, Pontryand Stiefel-Whitney classes are precise enough to play the same role as the Maslov classes when one replaces the base space X of the symplectic bundle, by S 7 X +the seventh topological suspension of X +the compactification of X.