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arXiv:math/0301180 [math.AT]AbstractReferencesReviewsResources

A generalization of the topological Brauer group

A. V. Ershov

Published 2003-01-16, updated 2005-11-18Version 6

In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber a matrix algebra. We also introduce some generalization of the Brauer group in the topological context and show that any its element can be represented as a locally trivial bundle with a group of invertible operators in a Hilbert space as the structure group. Finally, we discuss its possible applications in the twisted $K$-theory.

Comments: 34 pages. v5: The part concerning the generalized Brauer group has been completely rewritten. An application to twisted $K$-theory is added
Categories: math.AT, math.KT
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