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Studying the topological aspects of M-branes in M-theory leads to variousstructures related to Wu classes. First we interpret Wu classes themselves astwisted classes and then define twisted notions of Wu structures. Thesegeneralize many known structures, including Pin^- structures, twisted Spinstructures in the sense of Distler-Freed-Moore, Wu-twisted differentialcocycles appearing in the work of Belov-Moore, as well as ones introduced bythe author, such as twisted Membrane and twisted String^c structures. Inaddition, we introduce Wu^c structures, which generalize Pin^c structures, aswell as their twisted versions. We show how these structures generalize andencode the usual structures defined via Stiefel-Whitney classes.

Twisted topological structures related to M-branes II: Twisted Wu and Wu^c structures