The K-theory of relative group C*-algebras

Jintao Deng µË½ðÌÎ

*(University at Buffalo SUNY)*

10:00-11:00, May 22, 2024 Science Building A503

__Abstract:__

For the Dirac operator on a manifold with boundary, we can define its relative higher index which lies in the K-theory of the relative group $C^*$-algebra of fundamental groups. The relative Baum-Connes conjecture claims that a certain relative assembly map is an isomorphism. It provides an algorithm of the computation of the K-theory of relative group C*-algebras. In my talk, I will present several cases when the relative assembly maps are isomorphic (or injective). The strong relative Novikov conjecture states that the relative assembly map is injective. I will also talk about the applications of the strong Novikov conjecture in geometry and topology, especially about the relative higher signatures of manifolds with boundary. This is based on a joint work with G. Tian, Z. Xie and G. Yu.

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