Twisted Roe Algebras and the Coarse Baum-Connes Conjecture

Abstract: The coarse Baum-Connes conjecture claims that certain topological K-homology and the K-theory of Roe algebras associated to metric spaces are isomorphic via the index map. It provides algorithm to compute the higher indices for elliptic operators on non-compact Riemannian manifolds. The higher index is an element of the K-theory of the Roe algebra. To understand Roe algebras, we introduced a notion of twisted Roe algebras and a twisted coarse Baum-Connes conjecture. In the talk, I will cover basic properties of the twisted Roe algebras and the K-theory for the twisted algebras associated with metric spaces with a coarsely embeddable fibration structure. As an application, the coarse Baum-Connes conjecture holds for a finitely generated group which is an extension of coarsely embeddable groups. This is based on a joint work with Liang Guo.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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Noncommutative geometry in NYC

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