The coarse Baum-Connes conjecture is an important problem in index theory with powerful applications including the Novikov Conjecture. The conjecture is known to hold for many classes of groups and metric spaces and so far the only known counterexamples are expander graphs.

In this talk I will explain how spectral gaps for cohomological Laplacians in higher degrees lead to obstructions to surjectivity of the coarse assembly map. 

 

This is joint work with Kang Li and Sanaz Pooya.

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