vix.ing · top · new · best · stats

Growth tightness for groups with contracting elements

2013/01/31 by Wenyuan Yang
Mathematics · #math.GR #msc:20F65 #msc:20F67

paper · pdf · doi:10.1017/s0305004114000322

published as Math. Proc. Camb. Phil. Soc. 157 (2014) 297-319 · 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

arxiv created 2014/01/10 · arxiv updated 2019/02/20

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.

Citations