Generating the Johnson filtration II: finite generation
Geometric Topology
2017-11-16 v2 Group Theory
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.
Keywords
Cite
@article{arxiv.1704.01529,
title = {Generating the Johnson filtration II: finite generation},
author = {Thomas Church and Andrew Putman},
journal= {arXiv preprint arXiv:1704.01529},
year = {2017}
}
Comments
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