Title: Lecture 2. Asymptotic Dimension of Spaces and Groups
Speaker: Mladen Bestvina - University of Utah
Abstract: Gromov defined the notion of asymptotic dimension, which is a quasi-isometry invariant of spaces and groups. It is the large-scale analog of the usual covering dimension in topology. Computing it for a particular group, or even deciding if it is finite, is in general difficult. I will present some examples, e.g. Gromov's theorem that hyperbolic groups have finite asymptotic dimension, and outline a proof that mapping class groups have finite asymptotic dimension. This talk is based on my work with Ken Bromberg and Koji Fujiwara.