Geometry & Topology Seminar: Relative higher index theory on quotients of Roe algebras and directional obstructions to positive scalar curvature

Abstract: We formulate the relative coarse Baum-Connes conjecture and the relative coarse Novikov conjecture for general metric spaces as a program to compute the K-theory of the quotients of the Roe algebras modulo specific ideals. This study is motivated by the existence problem of positive scalar curvature metric on non-compact complete Riemannian manifolds, with a focus on their asymptotic behavior along certain directions at infinity. Under the assumption that the metric space admits a relative version of fibered coarse embedding into Hilbert space or lp-space, we establish the validity of these conjectures. This is joint work with Liang Guo and Chen Zhang.

Host: Xiang Tang