Local Index Theory over Foliation Groupoids
نویسنده
چکیده
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 Ω∗B associated to G. The proof is by means of superconnections in the framework of noncommutative geometry.
منابع مشابه
Local index theory over étale groupoids
We give a superconnection proof of Connes’ index theorem for proper cocompact actions of étale groupoids. This includes Connes’ general foliation index theorem for foliations with Hausdor¤ holonomy groupoid.
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