Outer space for RAAGs

2020/07/19 by Bregman, Corey, Charney, Ruth, Vogtmann, Karen
#20F28 #20F36 #20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2007.09725

Abstract

For any right-angled Artin group A_Γ we construct a finite-dimensional space O_Γ on which the group Out(A_Γ) of outer automorphisms of A_Γ acts with finite point stabilizers. We prove that O_Γ is contractible, so that the quotient is a rational classifying space for Out(A_Γ). The space O_Γ blends features of the symmetric space of lattices in ℝⁿ with those of Outer space for the free group F_n. Points in O_Γ are locally CAT(0) metric spaces that are homeomorphic (but not isometric) to certain locally CAT(0) cube complexes, marked by an isomorphism of their fundamental group with A_Γ.

Related

• Outer space and finiteness properties for symmetric automorphisms of RAAGs, and generalisations
• Finite groups of untwisted outer automorphisms of RAAGs
• Subgroups and quotient groups of automorphism groups of RAAGs
• Commensurability of groups quasi-isometric to RAAG's
• Quasi-isometry classification of right-angled Artin groups II: several infinite out cases