Category Archives: Expanded Outline (EO)

EO: embedding graph manifold groups in products of trees

Posted on March 25, 2012 by Alex Sisto

This post is based on this paper with David Hume. As discussed here, it is a nice property for a group to be quasi-isometrically embeddable in a product of finitely many trees. Graph manifolds are certain 3-manifolds, and if you … Continue reading →

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EO: contracting elements

Posted on March 5, 2012 by Alex Sisto

In this post I’ll talk about this paper. There are many groups that have been known for quite a while to “look like” hyperbolic groups, but only in certain “directions”. Examples of such directions are (the axes of ) rank … Continue reading →

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BI(+EO): quasi-isometric rigidity

Posted on January 29, 2012 by Alex Sisto

There are a few types of quasi-isometric rigidity results. I will talk about results of the following kinds: 1) self-quasi-isometries of such-and-such space or group (coarsely) preserve some structure, usually a collection of (left cosets) of subgroups 2) if a … Continue reading →

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EO: “hierarchy paths” for graph manifold groups

Posted on January 15, 2012 by Alex Sisto

I’d like to tell you about a certain family of bilipschitz paths in universal covers of graph manifolds with nice “combinatorial” properties that I used here and later here, and that hopefully will turn out to be useful in other … Continue reading →

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

Posted on December 28, 2011 by Alex Sisto

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

Posted on December 22, 2011 by Alex Sisto

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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