Welcome! Basic info about me and this blog can be found in the "about me and this blog" page.
- Brief Introduction (BI)
- Expanded Outline (EO)
- hyperbolicity of complexes
- Just for fun
- random walks
- Why not donating your paper to the public domain?
Author Archives: Alex Sisto
Hey everybody, it’s been a while… This post is about the notion of hierarchically hyperbolic space we defined with Jason Behrstock and Mark Hagen in this paper, which is a generalisation of the notion of (Gromov-)hyperbolic space. The main examples … Continue reading
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 described the Hensel-Przytycki-Webb proof that curve graphs are (uniformly) hyperbolic. Their methods actually apply to the arc graph, and then they used a clever evil trick due to Harer that involves adding an artificial puncture to … 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 tell you about a property of random walks on hyperbolic groups. To make a random walk on a group just start from the identity in the Cayley graph, then move to a neighbor with uniform probability … Continue reading
Real life model of the L-surface, realised by Mark Pedron with the help of Dawid Kielak. Yeah, too much light, I know… Clearer one: Explanation on the blackboard: The cone point. Behold the negative curvature!
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