Endomorphisms of Relatively Hyperbolic Groups

By Igor Belegradek, Andrzej Szczepanski. International journal of algebra and computation, 2008

406 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/574f6003b045b6efe22126d471fbbaf43a4164e4

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Citations in the corpus

Trees of cylinders and canonical splittings (2008, result): “lementary. Lemma 3.3. Co-elementarity is an equivalence relation on E. Proof. Let X be a proper hyperbolic metric space on which G acts properly discontinuously by isometries (not cocompactly), as in [Bow99]. We claim that two inﬁnite elementary subgroups A and B are co-elementary if and only if the”
On hyperbolicity of free splitting and free factor complexes (2012, background): “12 in [7] does not impose the “sufficiently separated” requirement.”
Projections and relative hyperbolicity (2010, methodology): “appeared before this one, beginning with the initial one due to M. Gromov in [Gr 2]; other equivalent denitions and developments of the theory of relatively hyperbolic groups may be found in [Bo 1], [Fa], [Da 1], [Ya], [Os 1]. Those denitions, however, are not fully \geometric" in that they are”
ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, background): “y, we are able to deal with groups which are “negatively curved” with respect to a collection of “small” subgroups, which includes, primarily, the widely studied class of relatively hyperbolic groups [3, 13]. The result and its proof are inspired by Ozawa’s general semi-solidity theorem (Theorem 15.”
Actions of finitely generated groups on R-trees (2006, background): “Actions on R-trees are also a main ingredient in Sela’ approach to acylindrical accessibility [32] (see [11] or [23] for alternative approaches) and in some studies of morphisms of a given group to a (relatively) hyperbolic group [33, 2, 12].”
Growth tight actions (2014, background): “5 [Bowditch 2012; Groves and Manning 2008; Sisto 2012].”
The SQ-universality and residual properties of relatively hyperbolic groups (2006, background): “We recall the definition of relatively hyperbolic groups suggested in [20] (for equivalent definitions in the case of finitely generated groups see [3,5, 6 ]).”
Weak Amenability of Hyperbolic Groups (2007, background): “Is it possible to construct a family of uniformly bounded representations as it is done in [Do, PS]? Is it true that a group which is hyperbolic relative to weakly amenable groups is again weakly amenable? There is no serious difficulty in extending Theorem 1 to (uniformly) fine hyperbolic graphs in”
Quasiconvexity in the Relatively Hyperbolic Groups (2011, background): “he actions of the groups of homeomorphisms of spheres, discontinuous outside a zero-dimensional set [GM87]. An important class of groups form relatively hyperbolic groups (RHG for short). B. Bowditch [Bo97] proposed a construction of the “boundary” for such gr oups. This is a compactum where the gro”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “, [30]) and both claims follow immediately from Theorem 6.”