Metrics on diagram groups and uniform embeddings in a Hilbert space

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dc.creatorArzhantseva, Goulnara
dc.creatorGuba, Victor
dc.creatorSapir, Mark
dc.date2004-11-26
dc.date2005-04-19
dc.date.accessioned2026-07-07T05:14:45Z
dc.date.available2026-07-07T05:14:45Z
dc.descriptionWe give first examples of finitely generated groups having an intermediate, with values in (0,1), Hilbert space compression (which is a numerical parameter measuring the distortion required to embed a metric space into Hilbert space). These groups include certain diagram groups. In particular, we show that the Hilbert space compression of Richard Thompson's group $F$ is equal to 1/2, the Hilbert space compression of the restricted wreath product $Z\wr Z$ is between 1/2 and 3/4, and the Hilbert space compression of $Z\wr (Z\wr Z)$ is between 0 and 1/2. In general, we find a relationship between the growth of $H$ and the Hilbert space compression of $Z\wr H$.
dc.description20 pages, Theorem 1.13 and Lemma 3.7. are new
dc.identifierhttps://arxiv.org/abs/math/0411605
dc.identifierhttp://arxiv.org/abs/math/0411605
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73395
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20F65
dc.titleMetrics on diagram groups and uniform embeddings in a Hilbert space
dc.typetext

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