Relatively hyperbolic groups: geometry and quasi-isometric invariance

By Cornelia Drutu. 2006

91 citations recorded by the source corpus.

In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar to the one of hyperbolicity, relying on the existence for every quasi-geodesic triangle of a central left coset of peripheral subgroup.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f0c0a0c5aa68d082f24804aa2f804cfb0564bbd6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Vincent Guirardel
2. Alessandro Sisto
3. V. Gerasimov
4. Denis V. Osin
5. L. Potyagailo
6. Franccois Dahmani
7. D. Groves
8. Ashot Minasyan

In Geometry and Topology

1. Alessandro Sisto
2. Denis V. Osin
3. Vincent Guirardel
4. Franccois Dahmani
5. V. Gerasimov
6. L. Potyagailo
7. Jason A. Behrstock
8. Mark F. Hagen

In Mathematical Physics

1. Alessandro Sisto
2. Denis V. Osin
3. Vincent Guirardel
4. Franccois Dahmani
5. V. Gerasimov
6. Mark F. Hagen
7. L. Potyagailo
8. Jason A. Behrstock

Citations in the corpus

• Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups. (2009, methodology): “The proof of Theorem B does not use [Dr] and [BDM] and considers directly the general case.”
• On Convex Projective Manifolds and Cusps (2011, unknown): “It follows from Druţu [28] Theorem 1.”
• On metric relative hyperbolicity (2012, methodology): “[Dru09] The geodesic metric space X is hyperbolic relative to the collection of subsets P, called peripheral sets, if P satisfies (α1) and (α2) and X is (∗)−asymptotically tree-graded with respect to P.”
• Growth tight actions (2014, unknown): “[27, 57]).”
• Quasi-convexity of hyperbolically embedded subgroups (2013, unknown): “In the case of relatively hyperbolic groups, it has been the development of the theory of relatively hyperbolic metric spaces started in [DS05] that lead to the proof of quasi-isometric rigidity, at first with additional hypotheses in [DS05] and then in general in [Dru09].”
• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “In the full generality this fact was proved by Drutu in [50] (see also [53] for a particular case).”