Local index theory over foliation groupoids

• Autores: Alexander Gorokhovsky, John Lott
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 204, Nº 2, 2006, págs. 413-447
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.05.018
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• Resumen

  • We give a local proof of an index theorem for a Dirac-type operator that is invariant with respect to the action of a foliation groupoid G. If M denotes the space of units of G then the input is a G-equivariant fiber bundle P?M along with a G-invariant fiberwise Dirac-type operator D on P. The index theorem is a formula for the pairing of the index of D, as an element of a certain K-theory group, with a closed graded trace on a certain noncommutative de Rham algebra associated to G. The proof is by means of superconnections in the framework of noncommutative geometry.