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Twisted longitudinal index theorem for foliations

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Speaker: 
Bryan Wang
Affiliation: 
Australian National U.
Date: 
Tue, 22/06/2010 - 14:30 - 15:00
Location: 
MPIM Lecture Hall

I report on the joint work with Paulo Carrillo-Rouse. For a foliation with a twisting on its leaf space, we establish the equivalence between the twisted topological index and the twisted analytic index, both taking values in the K-theory of the twisted C*-algebra of the honolomy groupoid. We also develop a notion of geometric cycles and the geometric K-homology for a foliation with a twisting. As an application of our twisted longitudinal index theorem, we

show that a twisted version of Baum-Connes assembly map is well-defined, and is expected to be an isomorphism whenever the untwisted assembly map is an isomorphism.

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