On finite generation of the Johnson filtrations

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.

37 pages, 3 figures. Major revision (especially to Section 5), to appear in JEMS

References in corpus (2)

• Dimension of the Torelli group for Out(F_n)
• Notes on the Sigma invariants

Cited by in corpus (8)

• On the top homology group of Johnson kernel
• On the structure of the top homology group of the Johnson kernel
• A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces
• Alternative versions of the Johnson homomorphisms and the LMO functor
• Alexander invariants and cohomology jump loci in group extensions
• Quasi-homomorphisms on mapping class groups vanishing on a handlebody group
• Effective finite generation for [IA_n,IA_n] and the Johnson kernel
• Lower central subgroups of a free group and its subgroup