Chern character for twisted K-theory of orbifolds

Jean Louis Tu, Ping Xu

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

For an orbifold X and α ∈ H3 (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.

Original languageEnglish (US)
Pages (from-to)455-483
Number of pages29
JournalAdvances in Mathematics
Volume207
Issue number2
DOIs
StatePublished - Dec 20 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Chern character for twisted K-theory of orbifolds'. Together they form a unique fingerprint.

Cite this