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Scientific article
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English

Metrics on diagram groups and uniform embeddings in a Hilbert space

Published inCommentarii mathematici Helvetici, vol. 81, no. 4, p. 911-929
Publication date2006
Abstract

We 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 $Zwr Z$ is between 1/2 and 3/4, and the Hilbert space compression of $Zwr (Zwr Z)$ is between 0 and 1/2. In general, we find a relationship between the growth of $H$ and the Hilbert space compression of $Zwr H$.

Classification
  • arxiv : math.GR
Note20 pages, Theorem 1.13 and Lemma 3.7. are new
Citation (ISO format)
ARZHANTSEVA, Goulnara N., GUBA, Victor, SAPIR, Mark. Metrics on diagram groups and uniform embeddings in a Hilbert space. In: Commentarii mathematici Helvetici, 2006, vol. 81, n° 4, p. 911–929. doi: 10.4171/cmh/80
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ISSN of the journal0010-2571
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