Automorphisms of two-dimensional right-angled Artin groups

Abstract

We study the outer automorphism group of a right-angled Artin group A_G in the case where the defining graph G is connected and triangle-free. We give an algebraic description of Out(A_G) in terms of maximal join subgraphs in G and prove that the Tits' alternative holds for Out(A_G). We construct an analogue of outer space for Out(A_G) and prove that it is finite dimensional, contractible, and has a proper action of Out(A_G). We show that Out(A_G) has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most general upper bound.

Bounds on vcd improved, proof of Tits' alternative added, expository improvements, typos corrected

Cited by in corpus (23)

• Quasiflats in CAT(0) complexes
• Peak reduction and finite presentations for automorphism groups of right-angled Artin groups
• The Tits alternative for the automorphism group of a free product
• Outer space for untwisted automorphisms of right-angled Artin groups
• Symplectic structures on right-angled Artin groups: between the mapping class group and the symplectic group
• Relative automorphism groups of right-angled Artin groups
• Groups quasi-isometric to RAAG's
• Vastness properties of automorphism groups of RAAGs
• Measure equivalence classification of transvection-free right-angled Artin groups
• Coarse-median preserving automorphisms
• The $R_{\infty }$-property for right-angled Artin groups
• Nielsen realisation for untwisted automorphisms of right-angled Artin groups
• Between buildings and free factor complexes: A Cohen-Macaulay complex for Out(RAAGs)
• Cube complexes and abelian subgroups of automorphism groups of RAAGs
• Outer actions of $\mathrm{Out}(F_n)$ on small right-angled Artin groups
• Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups
• Coarse cubical rigidity
• Outer automorphism groups of graph products: subgroups and quotients
• Finite groups of untwisted outer automorphisms of RAAGs
• Automorphism groups of cyclic products of groups
• Divisible cube complexes and finite-order automorphisms of RAAGs
• Dilatation of outer automorphisms of Right-angled Artin Groups
• Measure equivalence classification of right-angled Artin groups: the finite $\mathrm{Out}$ classes