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Cube complexes and abelian subgroups of automorphism groups of RAAGs
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Millard, Benjamin and Vogtmann, Karen (2021) Cube complexes and abelian subgroups of automorphism groups of RAAGs. Mathematical Proceedings of the Cambridge Philosophical Society, 170 (3). pp. 523-547. doi:10.1017/S0305004119000501 ISSN 0305-0041.
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WRAP-cube-complexes-abelian-automorphism-Vogtmann-2019.pdf - Accepted Version - Requires a PDF viewer. Download (964Kb) | Preview |
Official URL: https://doi.org/10.1017/S0305004119000501
Abstract
We construct free abelian subgroups of the group U(AΓ) of untwisted outer automorphisms of a right-angled Artin group, thus giving lower bounds on the virtual cohomological dimension. The group U(AΓ) was studied in [5] by constructing a contractible cube complex on which it acts properly and cocompactly, giving an upper bound for the virtual cohomological dimension. The ranks of our free abelian subgroups are equal to the dimensions of principal cubes in this complex. These are often of maximal dimension, so that the upper and lower bounds agree. In many cases when the principal cubes are not of maximal dimension we show there is an invariant contractible subcomplex of strictly lower dimension.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Abelian groups, Automorphisms, CW complexes | ||||||||
| Journal or Publication Title: | Mathematical Proceedings of the Cambridge Philosophical Society | ||||||||
| Publisher: | Cambridge University Press | ||||||||
| ISSN: | 0305-0041 | ||||||||
| Official Date: | May 2021 | ||||||||
| Dates: |
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| Volume: | 170 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 523-547 | ||||||||
| DOI: | 10.1017/S0305004119000501 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Mathematical Proceedings of the Cambridge Philosophical Society http://doi.org/10.1017/S0305004119000501 This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Copyright Holders: | © Cambridge Philosophical Society 2019 | ||||||||
| Date of first compliant deposit: | 24 October 2019 | ||||||||
| Date of first compliant Open Access: | 20 May 2020 | ||||||||
| RIOXX Funder/Project Grant: |
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