Generating the Johnson filtration II: finite generation

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.

14 pages. After completing this paper, we learned that Ershov independently obtained similar results. The subsequent joint paper, with improved results, is arXiv:1711.04779. This version remains as a permanent preprint and will not be submitted for publication

References in corpus (3)

• FI-modules and stability for representations of symmetric groups
• Cohomological Aspects of Magnus Expansions
• On finite generation of the Johnson filtrations