The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space

摘要

We introduce a notion of fibred coarse embedding into Hilbert space formetric spaces, which is a generalization of Gromov's notion of coarse embeddinginto Hilbert space. It turns out that a large class of expander graphs admitsuch an embedding. We show that the maximal coarse Baum-Connes conjecture holdsfor metric spaces with bounded geometry which admit a fibred coarse embeddinginto Hilbert space.