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arxiv: math/0209058 · v2 · submitted 2002-09-06 · 🧮 math.GR · math-ph· math.MP

Relative hyperbolicity and Artin groups

classification 🧮 math.GR math-phmath.MP
keywords artincollectiondefiningfarbgroupgroupshyperbolichyperbolicity
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Let $G=<a_1,..., a_n | a_ia_ja_i... = a_ja_ia_j..., i<j>$ be an Artin group and let $m_{ij}=m_{ji}$ be the length of each of the sides of the defining relation involving $a_i$ and $a_j$. We show if all $m_{ij}\ge 7$ then $G$ is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups $<a_i, a_j>$ for which $m_{ij}<\infty$.

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