Injections of Artin groups

• Autores: Robert W. Bell, Dan Margalit
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 82, Nº 4, 2007, págs. 725-752
• Idioma: inglés
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• Resumen

  • 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.