- 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 ...
Expand abstract - Publication status:
- Published
- Publisher copy:
- 10.1016/j.top.2005.03.003
-
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- Journal:
- TOPOLOGY
- Volume:
- 44
- Issue:
- 5
- Pages:
- 959-1058
- Publication date:
- 2004-05-03
- DOI:
- ISSN:
-
0040-9383
- URN:
-
uuid:890af457-dd59-44be-8e18-63c1348cb825
- Source identifiers:
-
27937
- Local pid:
- pubs:27937
- Copyright date:
- 2004
- Notes:
-
96 pages. The paper is accepted in "Topology". We revised the problem
section adding a couple of problems. We introduced concepts of constricted
(unconstricted, wide) groups and slow asymptotic cones. The Morse lemma for
relatively hyperbolic groups is improved thanks to a question from Chris
Hruska. A result about asymptotic cones of uniformly amenable groups and a
result about groups whose asymptotic cone is a real lines are added. We also
revised the text accordig to the comments of the referee and other readers of
the paper
Journal article
Tree-graded spaces and asymptotic cones of groups
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