Relative expander graphs and the coarse Baum-Connes conjecture

Qin Wang  (East China Normal University)

10:30-11:30,August 4,2023   ĸ¥ (Wenfu Building) 219


Expander graphs are highly connected and sparse graphs, which do not coarsely embed into Hilbert space, and are sources for counterexamples to the coarse Baum-Connes conjecture. Recently, G. Arzhantseva and R. Tessera introduce a notion of relative expander to give the first example of sequences of finite Cayley graphs of uniformly bounded degree, which do not coarsely embed into any Lp-spaces for any p > 1, yet do not contain any genuine expander. We show that the coarse Baum-Connes conjecture holds for all these relative expander graphs, solving an open problem raised by G. Arzhantseva and R. Tessera. This is joint work with Jintao Deng (University of Waterloo) and Guoliang Yu (TAMU).

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