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

Jinmin Wang Íõ½úÃñ

*(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.

__About the speaker:__

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