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Category Archives: Brief Introduction (BI)
BI: the BestvinaBrombergFujiwara construction
This post is about a remarkable construction due to BestvinaBrombergFujiwara. 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 DahmaniGuirardelOsin … Continue reading
Hyperbolicity of the curve graph: the proof from The Book
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 17hyperbolic. Hyperbolicity of curve graphs is a very very very useful* property because mapping class groups … Continue reading
BI: Finite decomposition complexity (is preserved by relative hyperbolicity)
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
BI: Guessing geodesics in hyperbolic spaces
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
Posted in guessing geodesics
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BI: Teichmüller space, part I
It is a remarkable fact that the group of orientationpreserving isometries of can be identified with the group of biholomorphisms of the unit disk in . [Fun fact: Poincaré said that he discovered (basically) this while stepping on a bus.] … Continue reading
Posted in Teichmuller space
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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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