Twisted K-theory of differentiable stacks

Jean Louis Tu, Ping Xu, Camille Laurent-Gengoux

Research output: Contribution to journalArticle

61 Citations (Scopus)

Abstract

In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S1-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure Kα i ⊗ Kβ j → Kα+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.

Original languageEnglish (US)
Pages (from-to)841-910
Number of pages70
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume37
Issue number6
DOIs
StatePublished - Jan 1 2004

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K-theory
Differentiable
KK-theory
Gerbe
Equivariant K-theory
K-group
Groupoids
Orbifold
Vector Bundle
Topological space
Periodicity
C*-algebra

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Tu, Jean Louis ; Xu, Ping ; Laurent-Gengoux, Camille. / Twisted K-theory of differentiable stacks. In: Annales Scientifiques de l'Ecole Normale Superieure. 2004 ; Vol. 37, No. 6. pp. 841-910.
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Twisted K-theory of differentiable stacks. / Tu, Jean Louis; Xu, Ping; Laurent-Gengoux, Camille.

In: Annales Scientifiques de l'Ecole Normale Superieure, Vol. 37, No. 6, 01.01.2004, p. 841-910.

Research output: Contribution to journalArticle

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