Towards a generalisation of hyperbolic spaces II
by
Indira Chatterji
Cornell University
Coauthors: Kim Ruane

Hyperbolicity in the sense of Gromov can be characterized by the phrase: "Every geodesic triangle is delta-thin". If the metric space in question is uniquely geodesic, then this is equivalent to saying "every triple of points forms the vertex set of a delta-thin geodesic triangle". However, if geodesics are not unique, then this notion, which we call L-delta, will be quite different. The first example is ZxZ with a minimal generating set, or more generally a CAT(0) cube complex endowed with the one skeleton metric. We shall examine the stability properties of this notion, show that some relatively hyperbolic groups in the sense of Gromov are L-delta spaces and how we "morally" perturb the metric on a CAT(0) space with isolated flats to get an L-delta space.

This talk is meant to be the second half of a two-part lecture on these spaces. Kim Ruane will have given the first part, where she will have discussed basic definitions, some examples and properties. We shall see further examples, properties and open questions.

Date received: September 10, 2004