Injections of Artin groups
arXiv:math/0501051
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.
21 pages, 8 figures, some corrections, new sections
References in corpus (5)
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- Automorphisms of surface braid groups
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- Combinatorial rigidity in curve complexes and mapping class groups
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