Local index theory over foliation groupoids |
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Authors: | Alexander Gorokhovsky John Lott |
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Institution: | a Department of Mathematics, UCB 395, University of Colorado, Boulder, CO 80309-0395, USA b Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA |
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Abstract: | 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. |
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Keywords: | 58J22 53C12 |
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