Hyperbolic groups with low-dimensional boundary
Michael Kapovich, Bruce Kleiner (2000)
Annales scientifiques de l'École Normale Supérieure
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Michael Kapovich, Bruce Kleiner (2000)
Annales scientifiques de l'École Normale Supérieure
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Ken'ichi Ohshika, Leonid Potyagailo (1998)
Annales scientifiques de l'École Normale Supérieure
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Pierre-Emmanuel Caprace, Yves de Cornulier, Nicolas Monod, Romain Tessera (2015)
Journal of the European Mathematical Society
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We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees...
J. Aramayona (2006)
Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales
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O'Neill, John C., Turner, Edward C. (2000)
The New York Journal of Mathematics [electronic only]
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Virpi Kauko (2000)
Fundamenta Mathematicae
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We discuss the tree structures of the sublimbs of the Mandelbrot set M, using internal addresses of hyperbolic components. We find a counterexample to a conjecture by Eike Lau and Dierk Schleicher concerning topological equivalence between different trees of visible components, and give a new proof to a theorem of theirs concerning the periods of hyperbolic components in various trees.
E. Rips, Z. Sela (1994)
Geometric and functional analysis
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Raúl Ures (1995)
Annales scientifiques de l'École Normale Supérieure
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