Right-angled Coxeter quandles and polyhedral products

DOI10.1090/PROC/14534zbMATH Open1483.20076arXiv1706.06209OpenAlexW2963217619WikidataQ128451374 ScholiaQ128451374MaRDI QIDQ5233951

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Publication date: 9 September 2019

Published in: (Search for Journal in Brave)

Abstract: To a Coxeter group $W$ one associates a quandle $X_W$ from which one constructs a group $mathrmAd(X_W)$. This group turns out to be an intermediate object between $W$ and the associated Artin group. By using a result of Akita, we prove that $mathrmAd(X_W)$ is given by a pullback involving $W$, and by using this pullback, we show that the classifying space of $mathrmAd(X_W)$ is given by a space called a polyhedral product whenever $W$ is right-angled. Two applications of this description of the classifying space are given.

Full work available at URL: https://arxiv.org/abs/1706.06209

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