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arXiv · 1909.03086

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

Matthew B. Day·Andrew W. Sale·Richard D. Wade
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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.

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Matthew B. Day, Andrew W. Sale, Richard D. Wade. 2019-09-06. Calculating the virtual cohomological dimension of the automorphism group of a RAAG. https://doi.org/10.1112/blms.12418

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