Monthly Archives: December 2011

EO: quasi-isometric embeddings of the hyperbolic plane in relatively hyperbolic groups

This post is based on a joint work with John MacKay. It is still an open question whether or not all non-virtually-free hyperbolic groups contain a surface group. This is actually related to (and AFAIK inspired by) an important open … Continue reading

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EO: Relative hyperbolicity and projections

In this post I’d like to tell you about the definition of relative hyperbolicity I gave in this paper. It is a definition that falls into the first family of definitions I described in this post, i.e. “relatively hyperbolic groups … Continue reading

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BI: Relatively hyperbolic groups, part 1

There are essentially three families of characterizations of relatively hyperbolic groups, corresponding to three different point of views. I’ll present two of them in this post, the ones I’m more familiar with, while in part 2 I’ll write about the … Continue reading

Posted in Brief Introduction (BI), relatively hyperbolic groups | Tagged | 3 Comments

BI: Tree-graded spaces

Tree-graded spaces have been defined by Cornelia DruĊ£u and Mark Sapir [DS]. They provide models for the coarse geometry of relatively hyperbolic groups, see example 2) below, but I’ll get back on this in some other post. I’ll assume that … Continue reading

Posted in Brief Introduction (BI), Tree-graded spaces | Tagged | 3 Comments