Bicombing the mapping class group
Harry Petyt (Bristol)
Abstract: One of the first generalisations of Gromov hyperbolicity for groups was the notion of semihyperbolicity, introduced by Alonso and Bridson in 1990, which asks for the group to have a well-behaved collection of quasigeodesics. I will discuss recent work with Thomas Haettel and Nima Hoda in which we show that mapping class groups and, more generally, hierarchically hyperbolic groups are semihyperbolic. This is done by constructing a new metric with interesting properties, which has several consequences for the group.