Compression of uniform embeddings into Hilbert space |
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| Authors: | N Brodskiy D Sonkin |
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| Institution: | a Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
b Department of Mathematics, University of Virginia, Charlottesville, VA 22903, USA |
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| Abstract: | 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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| Keywords: | primary 20F69 secondary 20F65 46C05 |
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