Elsevier

Advances in Mathematics

Volume 207, Issue 2, 20 December 2006, Pages 455-483
Advances in Mathematics

Chern character for twisted K-theory of orbifolds

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Abstract

For an orbifold X and αH3(X,Z), we introduce the twisted cohomology Hc(X,α) and prove that the non-commutative Chern character of Connes–Karoubi establishes an isomorphism between the twisted K-groups Kα(X)C and the twisted cohomology Hc(X,α). This theorem, on the one hand, generalizes a classical result of Baum–Connes, Brylinski–Nistor, and others, that if X is an orbifold then the Chern character establishes an isomorphism between the K-groups of X tensored with C, and the compactly-supported cohomology of the inertia orbifold. On the other hand, it also generalizes a recent result of Adem–Ruan regarding the Chern character isomorphism of twisted orbifold K-theory when the orbifold is a global quotient by a finite group and the twist is a special torsion class, as well as Mathai–Stevenson's theorem regarding the Chern character isomorphism of twisted K-theory of a compact manifold.

Keywords

Twisted cohomology
Twisted K-theory
Orbifold
Gerbe
Chern character

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Research partially supported by NSF grant DMS03-06665 and NSA grant 03G-142.