Quotient groups of IA-automorphisms of a free group of rank 3

@article{Metaftsis2018QuotientGO,
  title={Quotient groups of IA-automorphisms of a free group of rank 3},
  author={V. Metaftsis and Athanassios I. Papistas and I. Sevaslidou},
  journal={Int. J. Algebra Comput.},
  year={2018},
  volume={28},
  pages={115-131}
}
We prove that, for any positive integer c, the quotient group γc(M3)/γc+1(M3) of the lower central series of the McCool group M3 is isomorphic to two copies of the quotient group γc(F3)/γc+1(F3) of the lower central series of a free group F3 of rank 3 as ℤ-modules. Furthermore, we give a necessary and sufficient condition whether the associated graded Lie algebra gr(M3) of M3 is naturally embedded into the Johnson Lie algebra ℒ(IA(F3)) of the IA-automorphisms of F3. 
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2 Citations

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IA-automorphisms and Lie algebras related to the McCool group
On certain subgroups of the McCool group
TLDR
A subgroup of the automorphism group of Fn consisting of all automorphisms which induce the identity on Fn is assigned to IA(Fn), where Fn is a free group of rank n and IA (Fn) is the Automorphism Group.

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