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

100%

Cashen C. H.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

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.

The Boundary at Infinity of a Rough CAT(0) Space

75%

Buckley S. M., Falk K.

Analysis and Geometry in Metric Spaces

2014

tom 2

nr 1

We develop the boundary theory of rough CAT(0) spaces, a class of length spaces that contains both Gromov hyperbolic length spaces and CAT(0) spaces. The resulting theory generalizes the common features of the Gromov boundary of a Gromov hyperbolic length space and the ideal boundary of a complete CAT(0) space. It is not assumed that the spaces are geodesic or proper

Ograniczanie wyników

2 Analysis and Geometry in Metric Spaces

1 Buckley S. M.

1 Cashen C. H.

1 Falk K.

1 2016

1 2014

Wyniki wyszukiwania

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

The Boundary at Infinity of a Rough CAT(0) Space