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VIRTUALLY FIBERING RIGHT-ANGLED COXETER GROUPS

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  23 August 2019

Kasia Jankiewicz ,
Sergey Norin  and
Daniel T. Wise
Kasia Jankiewicz
Affiliation:
Department of Mathematics and Statsistics, McGill University, Montreal, Quebec, CanadaH3A 0B9 (kasia@math.uchicago.edu; snorine@gmail.com; wise@math.mcgill.ca)
Sergey Norin
Affiliation:
Department of Mathematics and Statsistics, McGill University, Montreal, Quebec, CanadaH3A 0B9 (kasia@math.uchicago.edu; snorine@gmail.com; wise@math.mcgill.ca)
Daniel T. Wise
Affiliation:
Department of Mathematics and Statsistics, McGill University, Montreal, Quebec, CanadaH3A 0B9 (kasia@math.uchicago.edu; snorine@gmail.com; wise@math.mcgill.ca)
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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.

Keywords

Coxeter groupsMorse theoryCoherent groups

MSC classification

Primary: 20F55: Reflection and Coxeter groups
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 3 , May 2021 , pp. 957 - 987
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Copyright
© Cambridge University Press 2019

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Footnotes

Research supported by NSERC.

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