Relative hyperbolicity and Artin groups. (English) Zbl 1080.20032
Summary: Let \(G=\langle a_1,\dots,a_n\mid a_ia_ja_i\cdots=a_ja_ia_j\cdots\), \(i<j\rangle\) 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 \(m_{ij}\geq 7\) then \(G\) is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups \(\langle a_i,a_j\rangle\) for which \(m_{ij}<\infty\).
MSC:
| 20F36 | Braid groups; Artin groups |
| 20F67 | Hyperbolic groups and nonpositively curved groups |
| 20F05 | Generators, relations, and presentations of groups |
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