Johnson homomorphisms and actions of higher-rank lattices on right-angled Artin groups
| Autor: | Wade, Richard D. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | J. London Math. Soc. (2013) 88 (3): 860-882 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/jlms/jdt044 |
| Popis: | Let G be a real semisimple Lie group with no compact factors and finite centre, and let $\Lambda$ be a lattice in G. Suppose that there exists a homomorphism from $\Lambda$ 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. Comment: 21 pages, 1 figure. Final draft. To appear in the Journal of the London Mathematical Society |
| Databáze: | arXiv |
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