o:1034936
Quasi-Isometries Need Not Induce Homeomorphisms of Contracting Boundaries with the Gromov Product Topology
en
We consider a â€˜contracting boundaryâ€™ 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.
2019-10-21T09:08:36.125Z
44
yes
46
Christopher
Cashen
University of Vienna
0000-0002-6340-469X
application/pdf
384771
http://phaidra.univie.ac.at/o:1034936
no
yes
16
70
1552253
Analysis and Geometry in Metric Spaces
4:278-281
4
278
281
De Gruyter
2016