Quasi-Isometries Need Not Induce Homeomorphisms of Contracting Boundaries with the Gromov Product Topology

Christopher H. Cashen. "Quasi-Isometries Need Not Induce Homeomorphisms of Contracting Boundaries with the Gromov Product Topology." Analysis and Geometry in Metric Spaces 4.1 (2016): 278-281, electronic only. <http://eudml.org/doc/286761>.

@article{ChristopherH2016,
abstract = {We consider a ‘contracting boundary’ of a proper geodesic metric space consisting of equivalence classes of geodesic rays that behave like geodesics in a hyperbolic space.We topologize this set via the Gromov product, in analogy to the topology of the boundary of a hyperbolic space. We show that when the space is not hyperbolic, quasi-isometries do not necessarily give homeomorphisms of this boundary. Continuity can fail even when the spaces are required to be CAT(0). We show this by constructing an explicit example.},
author = {Christopher H. Cashen},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Gromov boundary; quasi-isometry; contracting geodesic},
language = {eng},
number = {1},
pages = {278-281, electronic only},
title = {Quasi-Isometries Need Not Induce Homeomorphisms of Contracting Boundaries with the Gromov Product Topology},
url = {http://eudml.org/doc/286761},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Christopher H. Cashen
TI - Quasi-Isometries Need Not Induce Homeomorphisms of Contracting Boundaries with the Gromov Product Topology
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 278
EP - 281, electronic only
AB - We consider a ‘contracting boundary’ of a proper geodesic metric space consisting of equivalence classes of geodesic rays that behave like geodesics in a hyperbolic space.We topologize this set via the Gromov product, in analogy to the topology of the boundary of a hyperbolic space. We show that when the space is not hyperbolic, quasi-isometries do not necessarily give homeomorphisms of this boundary. Continuity can fail even when the spaces are required to be CAT(0). We show this by constructing an explicit example.
LA - eng
KW - Gromov boundary; quasi-isometry; contracting geodesic
UR - http://eudml.org/doc/286761
ER -