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

Authors

Matthew B. Day, University of Arkansas, FayettevilleFollow
Andrew W. Sale, University of Hawaii at Manoa
Richard D. Wade, University of Oxford

Document Type

Article

Publication Date

2-2021

Keywords

Cohomological dimension; Rank (graph theory); Basis (linear algebra)

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.

Citation

Day, M. B., Sale, A. W., & Wade, R. D. (2021). Calculating the virtual cohomological dimension of the automorphism group of a RAAG. Bulletin of the London Mathematical Society, 53 (1), 259-273. https://doi.org/10.1112/blms.12418

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.