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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hilbert space compression under direct limits and certain group extensions


Author: Dennis Dreesen
Journal: Proc. Amer. Math. Soc. 141 (2013), 421-436
MSC (2010): Primary 20F65; Secondary 20F67
Published electronically: June 7, 2012
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Abstract: We find bounds on the Hilbert space compression exponent of the limit of a directed metric system of groups. We also give estimates on the Hilbert space compression exponent of a group extension of a group $ H$ by a word-hyperbolic group or a group of polynomial growth.


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Dennis Dreesen
Affiliation: Katholieke Universiteit Leuven campus Kortrijk, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium – and – Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, 2009 Neuchâtel, Switzerland
Address at time of publication: Bât. M. de Hemptinne, á l’att. de Dennis Dreesen, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium
Email: dennis.dreesen@kuleuven-kortrijk.be; dennis.dreesen@unine.ch, dennis.dreesen@uclouvain.be

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11341-3
PII: S 0002-9939(2012)11341-3
Keywords: Hilbert space compression, hyperbolic groups, groups of polynomial growth, direct limits of groups
Received by editor(s): March 18, 2011
Received by editor(s) in revised form: June 16, 2011, and June 30, 2011
Published electronically: June 7, 2012
Additional Notes: The author is a research assistant for the Research Foundation - Flanders.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.