In mathematics, relatively hyperbolic groups form an important class of groups of interest for geometric group theory. The main purpose in their study...

In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely...

quasi-isometric rigidity of Baumslag–Solitar groups. The theory of word-hyperbolic and relatively hyperbolic groups. A particularly important development here...

notions of a hyperbolic group and of a relatively hyperbolic group and includes a significantly wider class of examples, such as mapping class groups and Out(Fn)...

finite groups, Gromov-hyperbolic groups, virtually torsion-free relatively hyperbolic groups with nilpotent parabolics, one-relator groups with non-trivial...

finitely generated groups in particular. Asymptotic cones also turn out to be a useful tool in the study of relatively hyperbolic groups and their generalizations...

In economics, hyperbolic discounting is a time-inconsistent model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis...

Sapir, Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups. Advances in Mathematics 217 (2008), no. 3, pp. 1313–1367 Igor...

G {\displaystyle \partial G} is a convergence group action. The action of a relatively hyperbolic group G {\displaystyle G} by translations on its Bowditch...

Cornelia; Sapir, Mark V. (2008). "Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups". Advances in Mathematics. 217 (3):...

properties of the group. Finitely presented groups satisfying sufficiently strong small cancellation conditions are word hyperbolic and have word problem...

alternating link is hyperbolic, i.e. the link complement has a hyperbolic geometry, unless the link is a torus link. Thus hyperbolic volume is an invariant...

rank problem is undecidable for word hyperbolic groups. The rank problem is decidable for torsion-free Kleinian groups. The rank problem is open for finitely...

Druţu, Cornelia; Sapir, Mark (2008), "Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups", Advances in Mathematics, 217 (3):...

continuous group-equivariant maps between the boundaries of two hyperbolic metric spaces extending a discrete isometric actions of the group on those spaces...

torsion-free group, always results in an SQ-universal group. Any non-elementary group that is hyperbolic with respect to a collection of proper subgroups is...

case of relatively hyperbolic groups and played a key role in the solution of the isomorphism problem for toral relatively hyperbolic groups. In his work...

theory of word-hyperbolic groups. In his 1987 monograph "Hyperbolic groups" Gromov proved that a finitely presented group is word-hyperbolic if and only...

of the asymptotic cones of relatively hyperbolic groups. This point of view allows for a notion of relative hyperbolicity that makes sense for geodesic...

the hyperbolic plane. At the same time, other challenges would be practically impossible in Euclidean, but are relatively easy in the hyperbolic world...

of comets (bodies that travel in elliptical, parabolic, and sometimes hyperbolic orbits and display a tail behind them) listed by type. Comets are sorted...

Druţu, Cornelia; Sapir, Mark (2008). "Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups". Advances in Mathematics. 217 (3):...

finitely generated groups in particular. Asymptotic cones also turn out to be a useful tool in the study of relatively hyperbolic groups and their generalizations...

Bowditch's PhD student Yaman gave a topological characterisation of relatively hyperbolic groups. Much of Bowditch's work in 2000s concerns the study of the curve...

MR 2146189. Osin, Densi (2005). "Asymptotic dimension of relatively hyperbolic groups". International Mathematics Research Notices. 2005 (35): 2143–61...

coprime (relatively prime) to n from the set { 0 , 1 , … , n − 1 } {\displaystyle \{0,1,\dots ,n-1\}} of n non-negative integers form a group under multiplication...

of relatively hyperbolic groups using geodesic triangles, similar to the one of hyperbolic groups. A classification of relatively hyperbolic groups up...

nilpotent groups, two elements having relatively prime orders must commute. It is also true that finite nilpotent groups are supersolvable. The concept is...

finite index n. Every abelian subgroup of a Gromov hyperbolic group is virtually cyclic. A profinite group is called procyclic if it can be topologically...

isoperimetric function approach to the theory of relatively hyperbolic groups. Geometric group theory Presentation of a group Seifert–Van Kampen theorem Alexander...