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

• Autorzy: Christopher H. Cashen
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Gromov boundary; quasi-isometry; contracting geodesic

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2015-05-06

zaakceptowano

2016-06-06

online

2016-09-23

Twórcy

autor

Christopher H. Cashen

• Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

Identyfikatory

DOI

10.1515/agms-2016-0011