Title (eng)

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

Author

Christopher Cashen   University of Vienna

Publishing

De Gruyter

Description

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.

Object languages

English

Date

2016

Rights

Creative Commons License
This work is licensed under a
CC BY 4.0 - Creative Commons Attribution 4.0 International License.

CC BY 4.0 International

http://creativecommons.org/licenses/by/4.0/

Member of the Collection(s) (2)

o:424738 Openaire v3.0 collection
o:168770 Open Access Collection