Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Uniform Hyperbolicity of Curve Graphs
Speaker: Kuwari Mahanta, TIFR, Mumbai
Date: November 4, 2024
Time: 15:25:00 Hours
Venue: A-369
Abstract: The curve graph of a compact orientable surface is a 1-dimensional simplical complex which was introduced in 1978 as a tool to study the Teichmüller spaces of Riemann surfaces. Since then it has also been used to study the hyperbolic structures of 3-manifolds and the mapping class group of surfaces. In 1999, Masur and Minsky showed that the curve graph is a $\delta$-hyperbolic space. Following this many authors have independently showed that there is an uniform $\delta$ for connected curve graphs. In this talk, we will look at a short and self-contained proof of the fact that curve graphs are uniformly hyperbolic. This proof was given by Hensel, Przytycki and Webb in [1]. One of the main tools that they use are a special kind of paths in curve graphs known as unicorn paths. [1] Hensel, S., Przytycki, P., and WEBB, R. C. H. 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs. J. Eur. Math. Soc. (JEMS) 17, 4 (2015), 755?762.
Title of Talk: Uniform Hyperbolicity of Curve Graphs
Speaker: Kuwari Mahanta, TIFR, Mumbai
Date: November 4, 2024
Time: 15:25:00 Hours
Venue: A-369
Abstract: The curve graph of a compact orientable surface is a 1-dimensional simplical complex which was introduced in 1978 as a tool to study the Teichmüller spaces of Riemann surfaces. Since then it has also been used to study the hyperbolic structures of 3-manifolds and the mapping class group of surfaces. In 1999, Masur and Minsky showed that the curve graph is a $\delta$-hyperbolic space. Following this many authors have independently showed that there is an uniform $\delta$ for connected curve graphs. In this talk, we will look at a short and self-contained proof of the fact that curve graphs are uniformly hyperbolic. This proof was given by Hensel, Przytycki and Webb in [1]. One of the main tools that they use are a special kind of paths in curve graphs known as unicorn paths. [1] Hensel, S., Przytycki, P., and WEBB, R. C. H. 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs. J. Eur. Math. Soc. (JEMS) 17, 4 (2015), 755?762.