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BY 3.0 license Open Access Published by De Gruyter Open Access September 23, 2016

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

  • Christopher H. Cashen

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.

References

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Received: 2015-5-6
Accepted: 2016-6-6
Published Online: 2016-9-23

© 2016 Christopher H. Cashen

This work is licensed under the Creative Commons Attribution 3.0 Public License.

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