Growth tightness for groups with contracting elements
Group Theory
2019-02-20 v2
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 nontrivial 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.
Cite
@article{arxiv.1301.5623,
title = {Growth tightness for groups with contracting elements},
author = {Wenyuan Yang},
journal= {arXiv preprint arXiv:1301.5623},
year = {2019}
}
Comments
23 pages, 2 figures.More general results are proved.Section 2 from the author's paper arXiv:1205.2994 is transformed in this paper, and will be deleted in that paper. Title changed to reflect these changes