TY - JOUR

T1 - Chern character for twisted K-theory of orbifolds

AU - Tu, Jean Louis

AU - Xu, Ping

N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (J.-L. Tu), [email protected] (P. Xu). 1 Research partially supported by NSF grant DMS03-06665 and NSA grant 03G-142.

PY - 2006/12/20

Y1 - 2006/12/20

N2 - 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.

AB - 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.

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U2 - 10.1016/j.aim.2005.12.001

DO - 10.1016/j.aim.2005.12.001

M3 - Article

AN - SCOPUS:33749049773

SN - 0001-8708

VL - 207

SP - 455

EP - 483

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -