On the virtual and residual properties of a generalization of Bestvina-Brady groups
On the virtual and residual properties of a generalization of Bestvina-Brady groups
Previously one of us introduced a family of groups GLM(S), parametrized by a finite flag complex L, a regular covering M of L, and a set S of integers. We give conjectural descriptions of when GLM(S) is either residually finite or virtually torsion-free. In the case that M is a finite cover and S is periodic, there is an extension with kernel GLM(S) and infinite cyclic quotient that is a CAT(0) cubical group. We conjecture that this group is virtually special. We relate these three conjectures to each other and prove many cases of them.
Residual finiteness, special cube complex, Bestvina-Brady group
2353-2373
Leary, Ian
57bd5c53-cd99-41f9-b02a-4a512d45150e
Vankov, Vladimir
dd4ebea0-800e-4d03-b1a6-b69388122a12
1 December 2022
Leary, Ian
57bd5c53-cd99-41f9-b02a-4a512d45150e
Vankov, Vladimir
dd4ebea0-800e-4d03-b1a6-b69388122a12
Leary, Ian and Vankov, Vladimir
(2022)
On the virtual and residual properties of a generalization of Bestvina-Brady groups.
Mathematische Zeitschrift, 302 (4), .
(doi:10.1007/s00209-022-03146-w).
Abstract
Previously one of us introduced a family of groups GLM(S), parametrized by a finite flag complex L, a regular covering M of L, and a set S of integers. We give conjectural descriptions of when GLM(S) is either residually finite or virtually torsion-free. In the case that M is a finite cover and S is periodic, there is an extension with kernel GLM(S) and infinite cyclic quotient that is a CAT(0) cubical group. We conjecture that this group is virtually special. We relate these three conjectures to each other and prove many cases of them.
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More information
Accepted/In Press date: 16 August 2022
e-pub ahead of print date: 27 September 2022
Published date: 1 December 2022
Additional Information:
Publisher Copyright:
© 2022, The Author(s).
Keywords:
Residual finiteness, special cube complex, Bestvina-Brady group
Identifiers
Local EPrints ID: 469748
URI: http://eprints.soton.ac.uk/id/eprint/469748
ISSN: 0025-5874
PURE UUID: a4690de6-5c9c-4126-b170-078f592d00de
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Date deposited: 23 Sep 2022 17:14
Last modified: 06 Jun 2024 04:19
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