Generating the Johnson filtration II: finite generation

TL;DR

This paper proves that all levels of the Johnson filtration and lower central series of Torelli groups and automorphism groups of free groups are finitely generated in a stable range, extending previous results.

Contribution

It generalizes finite generation results to all terms of the Johnson filtration and lower central series in a stable range.

Findings

All terms of the Johnson filtration are finitely generated in a stable range.

All terms of the lower central series are finitely generated in a stable range.

Extends previous finite generation results beyond the commutator subgroup.

Abstract

We prove that every term of the lower central series and Johnson filtrations of the Torelli subgroups of the mapping class group and the automorphism group of a free group are finitely generated in a stable range. This was originally proved for the commutator subgroup by Ershov-He.