Compression of uniform embeddings into Hilbert space
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spacehilbertcompressionhyperbolicanswerclosecomplexescube
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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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