Open access
Author
Date
2024-04-22Type
- Journal Article
ETH Bibliography
yes
Altmetrics
Abstract
A common feature of Coxeter groups and right-angled Artin groups is their solution to the word problem. Matthew Dyer introduced a class of groups, which we call Dyer groups, sharing this feature. This class includes, but is not limited to, Coxeter groups, right-angled Artin groups, and graph products of cyclic groups. We introduce Dyer groups by giving their standard presentation and show that they are finite-index subgroups of Coxeter groups. We then introduce a piecewise Euclidean cell complex Σ which generalizes the Davis–Moussong complex and the Salvetti complex. The construction of Σ uses simple categories without loops and complexes of groups. We conclude by proving that the cell complex Σ is CAT(0). Show more
Permanent link
https://doi.org/10.3929/ethz-b-000673046Publication status
publishedExternal links
Journal / series
Journal of Combinatorial AlgebraVolume
Pages / Article No.
Publisher
European Mathematical SocietySubject
Dyer groups; Coxeter groups; right-angled Artin groups; $\mathrm{CAT}(0)$ spacesMore
Show all metadata
ETH Bibliography
yes
Altmetrics