Calculating the virtual cohomological dimension of the automorphism group of a RAAG

Abstract

We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right-angled Artin group. The algorithm works in the relative setting; in particular it also applies to untwisted automorphism groups and basis-conjugating automorphism groups. The main new tool is the construction of free abelian subgroups of certain Fouxe-Rabinovitch groups of rank equal to their virtual cohomological dimension, generalizing a result of Meucci in the setting of free groups.

arXiv comment15 pages, 2 figures. Revised background on RORGs, small changes elsewhere. Accepted to appear in Bulletin of the LMS

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Cited by in corpus (4)

• Coarse-median preserving automorphisms
• A note on virtual duality and automorphism groups of right-angled Artin groups
• Divisible cube complexes and finite-order automorphisms of RAAGs
• Classifying spaces for families of abelian subgroups of braid groups, RAAGs and graphs of abelian groups