On finite generation of the Johnson filtrations

TL;DR

This paper proves that all levels of the Johnson filtrations for Torelli groups are finitely generated within a stable range, extending previous results to higher terms.

Contribution

It generalizes finite generation results of Johnson filtrations to all terms in a linear stable range, beyond the second term.

Findings

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

Extends previous finite generation results from the second term to all terms.

Provides new insights into the structure of Torelli subgroups.

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 is finitely generated in a linear stable range. This was originally proved for the second terms by Ershov and He.