Search

Your search keyword '"Gromov-hyperbolic space"' showing total 5 results
Start Over Descriptor "Gromov-hyperbolic space"
5 results on '"Gromov-hyperbolic space"'

2. A corrected quantitative version of the Morse lemma.

Author

Gouëzel, Sébastien and Shchur, Vladimir

Subjects
*EVIDENCE, *COMPUTERS, *MORSE theory, *SPACE, *CERTIFICATION
Abstract

There is a gap in the proof of the main theorem in the article [5] on optimal bounds for the Morse lemma in Gromov-hyperbolic spaces. We correct this gap, showing that the main theorem of [5] is true. We also describe a computer certification of this result. [ABSTRACT FROM AUTHOR]

Published
2019
Full Text
View/download PDF

3. A finiteness result for groups which quasi-act on hyperbolic spaces.

Author

Zuddas, Fabio

Abstract

Let ( X, d) be a Gromov-hyperbolic metric space endowed with a measure having finite entropy H and such that the measure of every ball of radius R > 0 is finite and bounded from below by a positive function of R. In this paper we look at the set Q( X; L, C, D) of the isomorphism classes of torsion-free groups Γ which admit a discrete, D-co-bounded ( L, C)-quasi-action on X ( D > 0, L ≥ 1, C ≥ 0) and we describe some algebraic conditions which, imposed on the groups Γ, define finite subsets of Q( X; L, C, D), provided C < ε for some ε > 0. As an example, these conditions are satisfied when Γ is assumed to admit a faithful, discrete, m-dimensional representation over some local field (in this case ε = ε( m, H, L)). In particular (set C = 0, L = 1), our results apply when the groups are assumed to act by isometries. [ABSTRACT FROM AUTHOR]

Published
2011
Full Text
View/download PDF

4. Hyperbolicité du graphe des rayons et quasi-morphismes sur un gros groupe modulaire

Author

Juliette Bavard, Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)

Subjects
37E30, Astrophysics::High Energy Astrophysical Phenomena, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Gromov-hyperbolic space, Dimension (graph theory), mapping class groups, 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], 57M60, Combinatorics, Mathematics - Geometric Topology, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], 0103 physical sciences, [MATH]Mathematics [math], 20F65, Mathematics - Dynamical Systems, 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics, Group (mathematics), 010102 general mathematics, surface homeomorphisms, Cantor sets, Surface (topology), Mapping class group, Cohomology, Cantor set, quasimorphisms, Bounded function, 010307 mathematical physics, Geometry and Topology, Mathematics - Group Theory
Abstract

The mapping class group $\Gamma$ of the complement of a Cantor set in the plane arises naturally in dynamics. We show that the ray graph, which is the analog of the complex of curves for this surface of infinite type, has infinite diameter and is hyperbolic. We use the action of $\Gamma$ on this graph to find an explicit non trivial quasimorphism on $\Gamma$ and to show that this group has infinite dimensional second bounded cohomology. Finally we give an example of a hyperbolic element of $\Gamma$ with vanishing stable commutator length. This carries out a program proposed by Danny Calegari., Comment: In french, 44 pages, 26 figures

Published
2016
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results