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Winter 1998 Presentations of Subgroups of Artin Groups
Jennifer Becker, Matthew Horak, Leonard VanWyk
Missouri J. Math. Sci. 10(1): 3-14 (Winter 1998). DOI: 10.35834/1998/1001003

Abstract

Let $A \Gamma$ be the Artin group based on the graph $\Gamma$, and let $\phi \colon A \Gamma \to {\mathbb Z}$ be a homomorphism which maps each of the standard generators of $A \Gamma$ to 0 or 1. We compute an explicit presentation for $\ker \phi$ in the general case. In the case where $\Gamma$ is a tree with a connected and dominating live subgraph, we prove $\ker \phi$ is a free group and we calculate its rank. In addition, if $A \Gamma$ is a 2-cone with live apex, we prove $\ker \phi$ is isomorphic to the Artin group on the base of the cone, and if $\Gamma$ is a special tree-triangle combination, we determine conditions on $\Gamma$ which ensure the finite presentation of $\ker \phi$.

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Jennifer Becker. Matthew Horak. Leonard VanWyk. "Presentations of Subgroups of Artin Groups." Missouri J. Math. Sci. 10 (1) 3 - 14, Winter 1998. https://doi.org/10.35834/1998/1001003

Information

Published: Winter 1998
First available in Project Euclid: 23 November 2019

zbMATH: 1097.20514
MathSciNet: MR1611316
Digital Object Identifier: 10.35834/1998/1001003

Rights: Copyright © 1998 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.10 • No. 1 • Winter 1998
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