Geometric approaches to braid groups and mapping class groups

Abstract

Geometric approaches to braid groups and mapping class groups AbstractThese are Lecture Notes of a course given by the author at the School Winter Braids, held at the Université de Pau et des Pays de L'Adour (France), on February 2015. It is explained how mapping class groups, and in particular braid groups, act on some interesting geometric spaces like the hyperbolic plane and the complex of curves, and how this allows to obtain some algebraic properties of the groups. A proof of the hyperbolicity of the graph of curves, following Hensel-Przytycki-Webb, is given.

Regular theory in complex braid groups

“…For instance the center of any finite index subgroup is determined in [DMM11] through the use of various Garside monoids, including the dual braid monoid. More recently, González-Meneses and Marin defined in [GM22] a general notion of parabolic subgroups of a complex braid group. They also studied these subgroups using the dual braid monoid notably.…”