COARSE EMBEDDINGS INTO A HILBERT SPACE, HAAGERUP PROPERTY AND POINCARÉ INEQUALITIES
COARSE EMBEDDINGS INTO A HILBERT SPACE, HAAGERUP PROPERTY AND POINCARÉ INEQUALITIES
We prove that a metric space does not coarsely embed into a Hilbert space if and only if it satisfies a sequence of Poincaré inequalities, which can be formulated in terms of (generalized) expanders. We also give quantitative statements, relative to the compression. In the equivariant context, our result says …