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Injections of Artin groups

Robert W. Bell·Dan Margalit
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Abstract

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 parameterized by a homeomorphism of a punctured sphere together with a map to the integers. We also give a generating set for the automorphism group of the pure braid group on at least 4 strands. The technique, following Ivanov, is to prove that every superinjective map of the complex of curves of a sphere with at least 5 punctures is induced by a homeomorphism.

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Robert W. Bell, Dan Margalit. 2006-05-17. Injections of Artin groups. https://arxiv.org/abs/math/0501051

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