Mapping class groups that do not virtually surject to the integers

Abstract: Mapping class groups of surfaces of genus at least 3 are perfect, but their finite-index subgroups need not be—they can have non-trivial abelianizations. A well-known conjecture of Ivanov states that a finite-index subgroup of a mapping class group of a sufficiently high genus has finite abelianization. We will discuss a proof of this conjecture, which goes through an equivalent representation-theoretic form of the conjecture due to Putman and Wieland.

group theorygeometric topologymetric geometry

Audience: researchers in the topic

McGill geometric group theory seminar