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2018 Outer actions of $\mathrm{Out}(F_n)$ on small right-angled Artin groups
Dawid Kielak
Algebr. Geom. Topol. 18(2): 1041-1065 (2018). DOI: 10.2140/agt.2018.18.1041

Abstract

We determine the precise conditions under which SOut ( F n ) , the unique index-two subgroup of Out ( F n ) , can act nontrivially via outer automorphisms on a RAAG whose defining graph has fewer than 1 2 n 2 vertices.

We also show that the outer automorphism group of a RAAG cannot act faithfully via outer automorphisms on a RAAG with a strictly smaller (in number of vertices) defining graph.

Along the way we determine the minimal dimensions of nontrivial linear representations of congruence quotients of the integral special linear groups over algebraically closed fields of characteristic zero, and provide a new lower bound on the cardinality of a set on which SOut ( F n ) can act nontrivially.

Citation

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Dawid Kielak. "Outer actions of $\mathrm{Out}(F_n)$ on small right-angled Artin groups." Algebr. Geom. Topol. 18 (2) 1041 - 1065, 2018. https://doi.org/10.2140/agt.2018.18.1041

Information

Received: 25 February 2017; Revised: 14 August 2017; Accepted: 21 November 2017; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859612
MathSciNet: MR3773746
Digital Object Identifier: 10.2140/agt.2018.18.1041

Subjects:
Primary: 20F65
Secondary: 20F28, 20F36

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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