Stable commutator length on big mapping class groups

Abstract

We study stable commutator length on mapping class groups of certain infinite‐type surfaces. In particular, we show that stable commutator length defines a continuous function on the commutator subgroups of such infinite‐type mapping class groups. We furthermore show that the commutator subgroups are open and closed subgroups and that the abelianizations are finitely generated in many cases. Our results apply to many popular infinite‐type surfaces with locally coarsely bounded mapping class groups.