TY - JOUR
T1 - Twisted K-theory of differentiable stacks
AU - Tu, Jean Louis
AU - Xu, Ping
AU - Laurent-Gengoux, Camille
N1 - Funding Information:
1Research partially supported by NSF grants DMS00-72171 and DMS03-06665.
PY - 2004
Y1 - 2004
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/14544273192
UR - https://www.scopus.com/inward/citedby.url?scp=14544273192&partnerID=8YFLogxK
U2 - 10.1016/j.ansens.2004.10.002
DO - 10.1016/j.ansens.2004.10.002
M3 - Article
AN - SCOPUS:14544273192
SN - 0012-9593
VL - 37
SP - 841
EP - 910
JO - Annales Scientifiques de l'Ecole Normale Superieure
JF - Annales Scientifiques de l'Ecole Normale Superieure
IS - 6
ER -