Relative automorphism groups of right-angled Artin groups
| Autor: | Matthew B. Day, Richard D. Wade |
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| Rok vydání: | 2019 |
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Classifying space
Group (mathematics) 010102 general mathematics Outer automorphism group Type (model theory) 16. Peace & justice Automorphism 01 natural sciences 20E36 20F36 Combinatorics Mathematics - Geometric Topology Mathematics::Group Theory Conjugacy class 0103 physical sciences Artin group Homomorphism 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics - Group Theory Mathematics |
| Popis: | We study the outer automorphism group of a right-angled Artin group $A_\Gamma$ with finite defining graph $\Gamma$. We construct a subnormal series for $Out(A_\Gamma)$ such that each consecutive quotient is either finite, free-abelian, $GL(n,\mathbb{Z})$, or a Fouxe-Rabinovitch group. The last two types act respectively on a symmetric space or a deformation space of trees, so that there is a geometric way of studying each piece. As a consequence we prove that the group $Out(A_\Gamma)$ is type VF (it has a finite index subgroup with a finite classifying space). The main technical work is a study of relative outer automorphism groups of RAAGs and their restriction homomorphisms, refining work of Charney, Crisp, and Vogtmann. We show that the images and kernels of restriction homomorphisms are always simpler examples of relative outer automorphism groups of RAAGs. We also give generators for relative automorphism groups of RAAGs, in the style of Laurence's theorem. Comment: 42 pages, 6 figures. Final arXiv version. Accepted for publication by the Journal of Topology |
| Databáze: | OpenAIRE |
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