Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9516322 | Topology | 2005 | 100 Pages |
Abstract
We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic cones, to find geometric properties of Cayley graphs of relatively hyperbolic groups, and to construct the first example of a finitely generated group with a continuum of non-Ï1-equivalent asymptotic cones. Note that by a result of Kramer, Shelah, Tent and Thomas, continuum is the maximal possible number of different asymptotic cones of a finitely generated group, provided that the Continuum Hypothesis is true.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Cornelia Druţu, Mark Sapir, with an Appendix by Denis Osinb and Mark Sapir with an Appendix by Denis Osinb and Mark Sapir,