A Combination Theorem for Relatively Hyperbolic Groups

By Emina Alibegović. 2003

77 citations recorded by the source corpus.

Given a graph of δ‐hyperbolic spaces, this paper gives sufficient conditions that ensure that the graph itself is δ‐hyperbolic. As an application, a simple proof is given to show that limit groups are relatively hyperbolic. 2000 Mathematics Subject Classification 57M07, 20F65.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dfb39fd2ad85c6a500489bfd4bf4356319e6623b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Dehn filling in relatively hyperbolic groups (2006, background): “... (2) Fundamental groups of geometrically finite hyperbolic manifolds are hyperbolic relative to the cusp subgroups; (3) Free products are hyperbolic relative to the free factors; (4) A group which acts properly and cocompactly on a CAT(0) space with isolated flats is hyperbolic relative to the st”
Quasiconvexity and relatively hyperbolic groups that split (2012, methodology): “rbolic context but through diverse methods. Dahmani proved a combination theorem for relatively hyperbolic groups using the convergence group approach [4]. Later Alibegovic´ proved similar results in [1] using a method generalizing parts of the Bestvina-Feighn approach. Osin reproved Dahman’s result”
A combination theorem for strong relative hyperbolicity (2006, background): “Again, in Alibegović’s combination theorem [1], an essential assumption is the compact intersection property.”
Boundary amenability of relatively hyperbolic groups (2005, background): “Hence, the relevant results in [Oz2][OP][Oz3] are applicable to such G. Examples of such groups include the fundamental groups of complete non-compact finite-volume Riemannian manifolds with pinched negative sectional curvature (which are hyperbolic relative to nilpotent cusp subgroups) [Fa] and lim”
RESEARCH ANNOUNCEMENT: THE STRUCTURE OF GROUPS WITH A QUASICONVEX HIERARCHY (2009, background): “This hierarchy allows one to prove that limit groups are hyperbolic relative to free abelian subgroups [11, 3].”
Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams (2005, background): “Recently there has been a large amount of interest in these groups (see [1, 8, 10, 12, 13, 24, 35], among others).”
Limit groups for relatively hyperbolic groups. I. The basic tools (2004, background): “Let Y denote the Cayley graph of Γ with respect to A, where each edge is isometric to the unit interval [0, 1].”