Journal article

### Tree-graded spaces and asymptotic cones of groups

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 finitely generated group with a continuum of non-$\pi_1$-equivalent asymptotic cones. Note that by a result of Kramer, Shelah, Tent ...

Publication status:
Published

### Access Document

Publisher copy:
10.1016/j.top.2005.03.003

### Authors

Journal:
TOPOLOGY
Volume:
44
Issue:
5
Pages:
959-1058
Publication date:
2004-05-03
DOI:
ISSN:
0040-9383
Source identifiers:
27937
Language:
English
Keywords:
Pubs id:
pubs:27937
UUID:
uuid:890af457-dd59-44be-8e18-63c1348cb825
Local pid:
pubs:27937
Deposit date:
2012-12-19