Geometry and Topology Seminar: "The relative Novikov conjecture"

Abstract: The relative Novikov conjecture concerns the manifolds with boundary. The conjecture claims that the relative higher signature is invariant under the orientation-preserving homotopy equivalence of pairs. In this talk, I will talk about the K-theory of the relative group $C^*$-algebras and show that the relative Novikov conjecture holds for a compact manifold with boundary when the fundamental group of the manifold is coarsely embeddable into Hilbert space and the homomorphism from the fundamental group of its boundary to the fundamental group of the manifold has the good kernel property. This is based on a joint work with Tian, Xie and Yu.

Host: Michael Landry