2005/05/12 by Jean-Louis Tu, Ping Xu, Tu, Jean-Louis +1 · 2 citations
Mathematics · #19L10 (Primary) 46L87 #46L80 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.math/0505267
openalex publication_date 2005/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an orbifold X and α∈ H3(X, Z), we introduce the twisted cohomology H^*c(X, α) and prove that the Connes-Chern character establishes an isomorphism between the twisted K-groups Kα^* (X) ⊗ C and twisted cohomology H^*c(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.