2,370 research outputs found
Peripheral structures of relatively hyperbolic groups
In this paper, we introduce and characterize a class of parabolically
extended structures for relatively hyperbolic groups. A characterization of
relative quasiconvexity with respect to parabolically extended structures is
obtained using dynamical methods. Some applications are discussed. The class of
groups acting geometrically finitely on Floyd boundaries turns out to be easily
understood. However, we also show that Dunwoody's inaccessible group does not
act geometrically finitely on its Floyd boundary.Comment: 30 page
Growth tightness for groups with contracting elements
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.Comment: 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 change
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