Chern character for twisted K-theory of orbifolds

• Autores: Jean-Louis Tu, Ping Xu
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 2, 2006, págs. 455-483
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.12.001
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• Resumen

  • For an orbifold and , we introduce the twisted cohomology and prove that the non-commutative Chern character of Connes¿Karoubi establishes an isomorphism between the twisted K-groups and the twisted cohomology . This theorem, on the one hand, generalizes a classical result of Baum¿Connes, Brylinski¿Nistor, and others, that if is an orbifold then the Chern character establishes an isomorphism between the K-groups of tensored with , 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.