Right-angled Coxeter quandles and polyhedral products
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- by Daisuke Kishimoto PDF
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Abstract:
To a Coxeter group $W$ one associates a quandle $X_W$ from which one constructs a group $\mathrm {Ad}(X_W)$. 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 $\mathrm {Ad}(X_W)$ is given by a pullback involving $W$, and by using this pullback, we show that the classifying space of $\mathrm {Ad}(X_W)$ 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.References
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Additional Information
- Daisuke Kishimoto
- Affiliation: Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan
- MR Author ID: 681652
- ORCID: 0000-0002-7837-8818
- Email: kishi@math.kyoto-u.ac.jp
- Received by editor(s): April 26, 2018
- Received by editor(s) in revised form: December 21, 2018
- Published electronically: May 9, 2019
- Additional Notes: The author was partly supported by JSPS KAKENHI (No. 17K05248).
- Communicated by: Mark Behrens
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3715-3727
- MSC (2010): Primary 20F55; Secondary 20F36, 20J06
- DOI: https://doi.org/10.1090/proc/14534
- MathSciNet review: 3993765