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Growth tightness for groups with contracting elements

Published online by Cambridge University Press:  30 July 2014

WEN-YUAN YANG
WEN-YUAN YANG*
Affiliation:
Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, P.R.China Le Département de Mathématiques de la Faculté des Sciences d'Orsay, Université Paris-Sud 11, France. e-mail: [email protected]
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Abstract

We establish growth tightness for a class of groups acting geometrically on a geodesic metric space and containing a contracting element. As a consequence, any group with non-trivial Floyd boundary are proven to be growth tight with respect to word metrics. In particular, all non-elementary relatively hyperbolic group are growth tight. This generalizes previous works of Arzhantseva-Lysenok and Sambusetti. Another interesting consequence is that CAT(0) groups with rank-1 elements are growth tight with respect to CAT(0)-metric.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 2 , September 2014 , pp. 297 - 319
Copyright
Copyright © Cambridge Philosophical Society 2014 

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