Compression of uniform embeddings into Hilbert space

2005/09/05 by N. Brodskiy, Brodskiy, N., D. Sonkin +1
Mathematics · #20F65 #20F69 #46C05 #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Topology (math.GT) #Group Theory (math.GR) #math.FA #math.GR #math.GT #msc:20F65 #msc:20F69 #msc:46C05

paper · pdf · doi:10.48550/arxiv.math/0509108

10 pages

arxiv created 2005/09/05 · arxiv updated 2009/12/01

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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