An l1-index theorem on manifold with boundary and positive scalar curvature

Jinmin Wang 王晋民  (Fudan University)

10:00-11:00, Dec 1, 2020   Zoom 467 658 1686

Abstract:

Given a compact spin manifold with boundary, if the metric has product structure and positive scalar curvature near the boundary, then the Dirac operator defines a higher index which lies in the K-theory of the reduced group C*-algebra of the fundamental group. It is open that whether the higher index lies in the image of the Baum?Connes assembly map. In this talk, we consider a lower bound of the scalar curvature which is related to the growth of the fundamental group. If the scalar curvature on the boundary is greater than the lower bound, then the higher index lies in the K-theory of the l^1 group algebra, which provides an application of the Bost conjecture for discrete groups. This is a joint work with Zhizhang Xie and Guoliang Yu.

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