We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a sphere with at least 5 punctures. In particular, we show that any injective homomorphism between these groups is given by a homeomorphism of a punctured sphere together with a map to the integers. The technique, following Ivanov, is to prove that every superinjective map of the curve complex of a sphere with at least 5 punctures is induced by a homeomorphism. We also determine the automorphism group of the pure braid group on at least 4 strands. © Swiss Mathematical Society.
CITATION STYLE
Bell, R. W., & Margalit, D. (2007). Injections of Artin groups. Commentarii Mathematici Helvetici, 82(4), 725–751. https://doi.org/10.4171/CMH/108
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