Monthly Archives: January 2012

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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BI: Asymptotic cones

Posted on January 22, 2012 by Alex Sisto

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 →

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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 →

Posted in special paths in graph manifolds | 1 Comment

BI: Thickness

Posted on January 2, 2012 by Alex Sisto

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 →

Posted in Brief Introduction (BI), thickness | Tagged | 1 Comment