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

Abstract

Studying the topological aspects of M-branes in M-theory leads to various structures related to Wu classes. First we interpret Wu classes themselves as twisted classes and then define twisted notions of Wu structures. These generalize many known structures, including Pin^- structures, twisted Spin structures in the sense of Distler-Freed-Moore, Wu-twisted differential cocycles appearing in the work of Belov-Moore, as well as ones introduced by the author, such as twisted Membrane and twisted String^c structures. In addition, we introduce Wu^c structures, which generalize Pin^c structures, as well as their twisted versions. We show how these structures generalize and encode the usual structures defined via Stiefel-Whitney classes.

20 pages

References in corpus (2)

• Geometry of Spin and Spin^c structures in the M-theory partition function
• Twisted topological structures related to M-branes

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• The Smith Fiber Sequence and Invertible Field Theories