Chern character for twisted Ktheory of orbifolds
Abstract
For an orbifold X and $\alpha \in H^3(X, Z)$, we introduce the twisted cohomology $H^*_c(X, \alpha)$ and prove that the ConnesChern character establishes an isomorphism between the twisted Kgroups $K_\alpha^* (X) \otimes C$ and twisted cohomology $H^*_c(X, \alpha)$. This theorem, on the one hand, generalizes a classical result of BaumConnes, BrylinskiNistor, and others, that if X is an orbifold then the Chern character establishes an isomorphism between the Kgroups of X tensored with C, and the compactlysupported cohomology of the inertia orbifold. On the other hand, it also generalizes a recent result of AdemRuan regarding the Chern character isomorphism of twisted orbifold Ktheory when the orbifold is a global quotient by a finite group and the twist is a special torsion class, as well as MathaiStevenson's theorem regarding the Chern character isomorphism of twisted Ktheory of a compact manifold.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 arXiv:
 arXiv:math/0505267
 Bibcode:
 2005math......5267T
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Differential Geometry;
 Mathematics  Mathematical Physics;
 Mathematics  Operator Algebras;
 Mathematical Physics;
 19L10 (Primary) 46L87;
 46L80 (Secondary)
 EPrint:
 26 pages. To appear in Advances in Mathematics