Boundary dimension in negatively curved spaces
type: Item
instance of: scholarly article
title: Boundary dimension in negatively curved spaces
zbMATH Open document ID: 0837.53037
DOI: 10.1007/BF01263486
author: Eric L. Swenson
published in: Geometriae Dedicata
publication date: 1996-05-13T00:00:00Z
review text: The paper deals with the so-called Gromov hyperbolic (negatively curved) spaces \(X\) which generalize the most important case of negatively curved groups, see \textit{M. Gromov} [Essays in group theory, Publ., Math. Sci. Res. Inst. 8, 75-263 (1987; Zbl 0634.20015)]. Gromov's condition on \(X\) to have finite-dimensional boundary \(\partial X\) is that \(X\) be a simplicial graph with bounded valence and unit length edges (which cover the case of the Cayley graph of a hyperbolic group, see also Prop. 6.2 in \textit{E. Ghys} and \textit{P. de la Harpe} [Sur les groupes hyperboliques d'après Mikhael Gromov, Prog. Math. 83, Boston, MA: Birkhäuser (1990; Zbl 0731.20025)]. The author gives a more general result which implies that such \(X\) with a cocompact isometry group action always has finite-dimensional boundary (the author's usage compact does not imply Hausdorff). As another result, the author gives an example of a negatively curved space \(X\) with infinite-dimensional boundary.
reviewed by: Boris N. Apanasov
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 806290
zbMATH Keywords: boundary dimension
zbMATH Keywords: Gromov hyperbolic spaces
MaRDI profile type: Publication
cites work: Q4865833
cites work: The Boundary of Negatively Curved Groups
cites work: Q4010477
cites work: Recognizing constant curvature discrete groups in dimension 3
cites work: Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
cites work: Q3772406
cites work: Hyperbolic elements in negatively curved groups
full work available at URL: https://doi.org/10.1007/bf01263486
OpenAlex ID: W2068750781
description: scientific article; zbMATH DE number 806290