6533b85cfe1ef96bd12bc876
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On the hyperbolic limit points of groups acting on hyperbolic spaces
Marco Pavonesubject
Discrete mathematicsPure mathematicsHyperbolic groupGeneral MathematicsHyperbolic 3-manifoldHyperbolic angleHyperbolic manifoldUltraparallel theoremRelatively hyperbolic groupMathematicsHyperbolic equilibrium pointHyperbolic treedescription
We study the hyperbolic limit points of a groupG acting on a hyperbolic metric space, and consider the question of whether any attractive limit point corresponds to a unique repulsive limit point. In the special case whereG is a (non-elementary) finitely generated hyperbolic group acting on its Cayley graph, the answer is affirmative, and the resulting mapg +↦g −, is discontinuous everywhere on the hyperbolic boundary. We also provide a direct, combinatorial proof in the special case whereG is a (non-abelian) free group of finite type, by characterizing algebraically the hyperbolic ends ofG.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-01-01 | Rendiconti del Circolo Matematico di Palermo |