WoG 2024 Talk 2.1: Juhun Baik - Topological normal generation of big mapping class groups

Speaker: Juhun Baik
Institution: KAIST

Title: Topological normal generation of big mapping class groups
Abstract: By Lanier and Margalit, any pseudo-Anosov map with stretch factor is less than $\sqrt{2}$ normally generates the mapping class group. Also, for closed surfaces of genus more than 2, any torsion element except hyperelliptic involution is a normal generator. We ask for the case of a big mapping class group, namely the mapping class group of infinite type surfaces. In this talk, I will first introduce the the topology of big mapping class groups. After that I will answer when the big mapping class group is topologically normally generated by one element, and give an upper bound of how many generators are needed to topologically normally generate the group.