Compression of uniform embeddings into Hilbert space

Details Compression of uniform embeddings into Hilbert space Compression of uniform embeddings into Hilbert space

2005-09-05

arxiv.org/abs/math/0509108v1

Mathematics

Group Theory

10 pages

Scientific paper

If one tries to embed a metric space uniformly in Hilbert space, how close to
quasi-isometric could the embedding be? We answer this question for finite
dimensional CAT(0) cube complexes and for hyperbolic groups. In particular, we
show that the Hilbert space compression of any hyperbolic group is 1.

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