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Compression functions of uniform embeddings of groups into Hilbert and Banach spaces

Contributors

Arzhantseva, Goulnara N.; Druţu, Cornelia; Sapir, Mark

Published in

Journal für die reine und angewandte Mathematik, vol. 2009, no. 633, p. 213-235

Collection

  • Open Access - Licence nationale de Gruyter

Publication date

2009

Abstract

We construct finitely generated groups with arbitrary prescribed Hilbert space compression alpha from the interval [0,1]. For a large class of Banach spaces E (including all uniformly convex Banach spaces), the E-compression of these groups coincides with their Hilbert space compression. Moreover, the groups that we construct have asymptotic dimension at most 3, hence they are exact. In particular, the first examples of groups that are uniformly embeddable into a Hilbert space (respectively, exact, of finite asymptotic dimension) with Hilbert space compression 0 are given. These groups are also the first examples of groups with uniformly convex Banach space compression 0.

Classification

  • arxiv : math.GR

UNIGE affiliation entities

Citation (ISO format)

ARZHANTSEVA, Goulnara N., DRUŢU, Cornelia, SAPIR, Mark. Compression functions of uniform embeddings of groups into Hilbert and Banach spaces. In: Journal für die reine und angewandte Mathematik, 2009, vol. 2009, n° 633, p. 213–235. doi: 10.1515/CRELLE.2009.066

Main files (2)

Article (Submitted version)
Article (Published version)
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Identifiers

Journal ISSN

0075-4102
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716downloads

Technical informations

Creation

30/06/2010 14:42:00

First validation

30/06/2010 14:42:00

Update

14/03/2023 15:55:36

Status update

14/03/2023 15:55:36

Last indexation

29/10/2024 16:15:57
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