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Chern character for twisted K-theory of orbifolds | | Jean-Louis Tu
; Ping Xu
; | | Date: |
12 May 2005 | | Subject: | K-Theory and Homology; Differential Geometry; Operator Algebras; Mathematical Physics MSC-class: 19L10 (Primary) 46L87, 46L80 (Secondary) | math.KT math-ph math.DG math.MP math.OA | | 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 Connes-Chern character establishes an isomorphism between the twisted K-groups $K_alpha^* (X) otimes C$ and twisted cohomology $H^*_c(X, alpha)$. 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. | | Source: | arXiv, math.KT/0505267 | | Services: | Forum | Review | PDF | Favorites | |
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