Towards a generalization of hyperbolic spaces
by
Kim Ruane
Tufts University
Coauthors: Indira Chatterji

Hyperbolicity in the sense of Gromov can be characterized by the phrase: Ëvery geodesic triangle is delta-thin". If the metric space in question is uniquely geodesic, then this is equivalent to saying ëvery 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 stabiity 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.

In this talk, we will discuss the basic definitions, some first examples, and several properties of L-delta spaces. This talk is meant to be the first half of a two-part lecture on these spaces. Indira Chatterji will give the second part where she will discuss more properties and open questions.

Date received: September 10, 2004