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This post is about a remarkable construction due to Bestvina-Bromberg-Fujiwara. It has been first used to show that the asymptotic dimension of Mapping Class Groups is finite, and it is quite useful, for example, in this great paper by Dahmani-Guirardel-Osin … Continue reading
In this post I’ll talk about a lovely paper by Sebastian Hensel, Piotr Przytycki and Richard Webb. They show that all curve graphs are 17-hyperbolic. Hyperbolicity of curve graphs is a very very very useful* property because mapping class groups … Continue reading
In this post I’ll define finite decomposition complexity (FDC) for you, tell you what it’s good for (Stable Borel Conjecture!) and point out that an argument by Osin shows that it is preserved by relative hyperbolicity. First, the motivation. Here … Continue reading
In this post I’ll discuss a cool lemma due to Brian Bowditch (from this paper) which is very useful when you want to show that a space is hyperbolic. The most direct way of showing that is hyperbolic is trying … Continue reading
It is a remarkable fact that the group of orientation-preserving isometries of can be identified with the group of bi-holomorphisms of the unit disk in . [Fun fact: Poincaré said that he discovered (basically) this while stepping on a bus.] … Continue reading
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