Category Archives: Expanded Outline (EO)

EO: embedding graph manifold groups in products of trees

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

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

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

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

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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