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

2017/01/10 by V. Metaftsis, Metaftsis, V., A. I. Papistas +3
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1701.02478

Abstract

We prove that, for any positive integer c, the quotient group γ_c(M₃)/γ_c+1(M₃) of the lower central series of the McCool group M₃ is isomorphic to two copies of the quotient group γ_c(F₃)/γ_c+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 \rm gr(M₃) of M₃ is naturally embedded into the Johnson Lie algebra \cal L(\rm IA(F₃)) of the IA-automorphisms of F₃.

Citations

• On Basis-Conjugating Automorphisms of Free Groups

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• Actions of automorphism groups of free groups on spaces of Jacobi diagrams. II