Wed, 24 Apr 2024
16:00
16:00
L6
Harmonic maps and virtual properties of mapping class groups
Ognjen Tošić
(University of Oxford)
Abstract
It is a standard result that mapping class groups of high genus do not surject the integers. This is easily shown by computing the abelianization of the mapping class group using a presentation. Once we pass to finite index subgroups, this becomes a conjecture of Ivanov. More generally, we can ask which groups admit epimorphisms from finite index subgroups of the mapping class group. In this talk, I will present a geometric approach to this question, using harmonic maps, and explain some recent results.