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Author Archives: Alex Sisto
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 quasiisometrically embeddable in a product of finitely many trees. Graph manifolds are certain 3manifolds, and if you … Continue reading
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
Posted in contracting elements
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Why not donating your paper to the public domain?
Breaking news: David Hume and I just managed to make sure that our paper will be in the public domain when published (by Proceedings of the AMS). We have been inspired by Saul Schleimer, who has been consistently dedicating his papers … Continue reading
BI: nonstandard analysis, a small investment
First of all, you can read about nonstandard analysis in a slightly more famous blog than my own, for example you can check out this post. I guess I should explain the quote “a small investment” by Isaac Goldbring (afaik). … Continue reading
Posted in nonstandard analysis
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BI(+EO): quasiisometric rigidity
There are a few types of quasiisometric rigidity results. I will talk about results of the following kinds: 1) selfquasiisometries of suchandsuch space or group (coarsely) preserve some structure, usually a collection of (left cosets) of subgroups 2) if a … Continue reading
BI: Asymptotic cones
This post contains an experimental exposition of asymptotic cones, I hope this will be vaguely understandable (feedback is warmly welcome!). Many (most?) researchers actually think of asymptotic cones in a way similar to the one I’ll present, rather than as … Continue reading
Posted in asymptotic cones
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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
Posted in special paths in graph manifolds
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BI: Thickness
Thick metric spaces were defined in this paper by Jason Behrstock, Cornelia Druţu and Lee Mosher as an obstruction for a group (actually, a metric space) to be (properly) relatively hyerbolic. Indeed, the notion of thickness provides a very interesting way of … Continue reading