Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compression of uniform embeddings into Hilbert space   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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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess