VIRTUALLY FIBERING RIGHT-ANGLED COXETER GROUPS. (23rd May 2021)

• Record Type: Journal Article
• Authors: Jankiewicz, Kasia; Norin, Sergey; Wise, Daniel T.
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 20:Number 3(2021)
• Page Start: 957
• Page End: 987
• Publication Date: 2021-05-23
• Subjects: Coxeter groups, -- Morse theory, -- Coherent groups; 20F55; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748019000422
• Languages: English
• ISSNs: 1474-7480

Abstract

Abstract: We show that certain right-angled Coxeter groups have finite index subgroups that quotient to $\mathbb{Z}$ with finitely generated kernels. The proof uses Bestvina–Brady Morse theory facilitated by combinatorial arguments. We describe a variety of examples where the plan succeeds or fails. Among the successful examples are the right-angled reflection groups in $\mathbb{H}^{4}$ with fundamental domain the 120-cell or the 24-cell.