The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Tree-graded spaces and asymptotic cones of groups
Open accessAbstract
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- π 1 -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.
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Cites
(2001) · Cited by 5,374
Metric Spaces of Non-Positive Curvature
Bridson, M. R., & Haefliger, A. (1999) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-662-12494-9 · Cited by 4,499
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Burago, D., Burago, Y., & Ivanov, S. (2001) · Graduate Studies in Mathematics · doi:10.1090/gsm/033 · Cited by 2,598
Gromov, M. (1987) · Mathematical Sciences Research Institute Publications · doi:10.1007/978-1-4613-9586-7_3 · Cited by 1,817
Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)
Gromov, M. (1981) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02698687 · Cited by 1,727
Manifolds of Nonpositive Curvature
Ballmann, W., Gromov, M., & Schroeder, V. (1985) · Progress in Mathematics · doi:10.1007/978-1-4684-9159-3 · Cited by 788
Structures métriques pour les variétés riemanniennes
Gromov, M. (1981) · Medical Entomology and Zoology · Cited by 518
Farb, B. (1998) · Geometric And Functional Analysis · doi:10.1007/s000390050075 · Cited by 451
Bowditch, Β. H. (2011) · International Journal of Algebra and Computation · doi:10.1142/s0218196712500166 · Cited by 389
Metadata
- Authors
- Druţu, C., & Sapir, M.
- Venue
- Topology
- Publisher
- Elsevier BV
- Published
- 2005-09
- Volume
- 44
- Issue
- 5
- Pages
- 959-1058
- ISSN
- 0040-9383 (ISSN-L)
- OpenAlex
- W1975757718
- Cited by
- 318
- References
- 17
- FWCI
- 25.86
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
