Artin relations in the mapping class group (Q431067)

In the article under review, the author studies certain relations in mapping class groups of surfaces between various multitwists. The author is particularly interested in Artin relations of length \(n\geq 2\), which are relations of the form \(xyx\cdots=yxy\cdots\), where each side has \(n\) letters occurring. The author proves that certain chains of simple closed curves on surfaces give rise to multitwists which generate Artin subgroups of the corresponding mapping class groups. The author establishes the results by direct computation and by Crisp's work on injective maps between Artin groups.