Twisted K theory of differentiable stacks

By J. Tu, P. Xu, C. Laurent-Gengoux. 2003

161 citations recorded by the source corpus.

Abstract In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S 1 -gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity, and the product structure K α i ⊗ K β j → K α + β i + j are derived. Our approach provides a uniform framework for studying various twisted K-theories including the usual twisted K-theory of topological spaces, twisted equivariant K-theory, and the twisted K-theory of orbifolds. We also present a Fredholm picture, and discuss the conditions under which twisted K-groups can be expressed by so-called “twisted vector bundles”. Our approach is to work on presentations of stacks, namely groupoids, and relies heavily on the machinery of K-theory (KK-theory) of C ∗ -algebras.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/987aec1bbf7373acbcc8ffc26dfdaa2bd29f1fff

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Parametrized homotopy theory (2004, methodology): “In the equivariant case, we rely on details in the general stack-theoretic treatment of Tu, Xu, and Laurent-Gengoux [164].”
Differentiable stacks and gerbes (2006, methodology): “Such a geometrical realization is crucial in applications to twisted K-theory [43, 44, 45].”