Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups☆

By Cornelia Drutu, Mark V. Sapir. 2006

56 citations recorded by the source corpus.

Abstract Tree-graded spaces are generalizations of R -trees. They appear as asymptotic cones of groups (when the cones have cut-points). Since many questions about endomorphisms and automorphisms of groups, solving equations over groups, studying embeddings of a group into another group, etc. lead to actions of groups on the asymptotic cones, it is natural to consider actions of groups on tree-graded spaces. We develop a theory of such actions which generalizes the well-known theory of groups acting on R -trees. As applications of our theory, we describe, in particular, relatively hyperbolic groups with infinite groups of outer automorphisms, and co-Hopfian relatively hyperbolic groups.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5200b91d310bdc9e898ed36b506273adeeec3fa6

How researchers see this paper

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

In Discrete Mathematics and Combinatorics

1. D. Groves
2. Denis V. Osin
3. A. Ol’shanskii
4. Mark V. Sapir
5. Cornelia Drutu
6. Shahar Mozes
7. Michael Hull
8. Alessandro Sisto

In Geometry and Topology

1. D. Groves
2. Denis V. Osin
3. Alessandro Sisto
4. Cornelia Drutu
5. Mark V. Sapir
6. A. Ol’shanskii
7. Jason A. Behrstock
8. Shahar Mozes

In Mathematical Physics

1. Denis V. Osin
2. D. Groves
3. Alessandro Sisto
4. Cornelia Drutu
5. A. Ol’shanskii
6. Mark V. Sapir
7. Shahar Mozes
8. Jason A. Behrstock

Citations in the corpus

• Lacunary hyperbolic groups (2007, methodology): “In [14], this program has been carried out for relatively hyperbolic groups (all asymptotic cones of relatively hyperbolic groups have cut points by a result of Druţu and Sapir [13]).”
• Limit groups for relatively hyperbolic groups. I. The basic tools (2004, methodology): “2The R-tree we construct is different to that constructed by Druţu and Sapir in [18].”
• Divergence in lattices in semisimple Lie groups and graphs of groups (2008, background): “…H has infinitely many homomorphisms into G that are pairwise non-conjugate in G, then H acts non-trivially on an asymptotic cone of G which in many cases implies that H acts non-trivially on a simplicial tree [DS06], and so H splits non-trivially into an amalgamated product or an HNN extension.”