Johnson homomorphisms and actions of higher-rank lattices on right-angled Artin groups

Details Johnson homomorphisms and actions of higher-rank lattices on right-angled Artin groups Johnson homomorphisms and actions of higher-rank lattices on right-angled Artin groups

2011-01-14

arxiv.org/abs/1101.2797v2

Mathematics

Group Theory

19 pages, 1 figure. There was an error in the proof of Theorem 3.8 of the previous draft, however this result has been indepen

Scientific paper

Let G be a real seimsimple Lie group with no compact factors and finite centre, and let $\Delta$ be a lattice in G. Suppose that there exists a homomorphism from $\Delta$ to the outer automorphism group of a right-angled Artin group $A_\Gamma$ with infinite image. We give an upper bound to the real rank of G that is determined by the structure of cliques in $\Gamma$. An essential tool is the Andreadakis-Johnson filtration of the Torelli subgroup $\mathcal{T}}(A_\Gamma)$ of $Aut(A_\Gamma)$. We answer a question of Day relating to the abelianisation of $\mathcal{T}}(A_\Gamma)$, and show that $\mathcal{T}}(A_\Gamma)$ and its image in $Out(A_\Gamma)$ are residually torsion-free nilpotent.

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