Spaces and Questions

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The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space (2012, background): “Gromov discovered that a metric space of expander graphs [29, 28] cannot be coarsely embedded into a Hilbert space [13].”
Finite part of operator K-theory for groups finitely embeddable into Hilbert space and the degree of non-rigidity of manifolds (2013, background): “However, Gromov’s monster groups are not coarsely embeddable into Hilbert space (Gromov [13] and Arzhantseva and Delzant [1]).”
Orbit Equivalence and Measured Group Theory (2010, background): “ dΦ on X: the simplicial distance associated with the graph structure in the classes of RΦ and dΦ = ∞ between two points in diﬀerent classes. This is a typical instance of what Gromov calls a mmspace [Gro00], i.e. a probability measure space (X,µ) together with a Borel function d : X × X → R+ ∪ {∞} ”