A longitudinal index theorem on an open foliation manifold

Xiang Tang   (Washington University at St Louis)

14:20-15:10, March 15, 2019   Science Building A510


In this talk, we will introduce the concept of Roe C*-algebra for a locally compact groupoid whose unit space is in general not compact, and that is equipped with an appropriate coarse structure and Haar system. Using Connes' tangent groupoid method, we will define an analytic index for an elliptic differential operator on a Lie groupoid equipped with additional metric structure, which takes values in the K-theory of the Roe C*-algebra. And we will discuss applications of our developments to longitudinal elliptic operators on an open foliated manifold. This is joint work with Rufus Willett and Yi-Jun Yao.

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