L'interprétation de la classe de Maslov dans la K-théorie Hermitienne et dans la théorie relative de Chern—Weil

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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 S7X+, the seventh topological suspension of X+, the compactification of X.

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