Injections of Artin groups

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)

• Automorphisms of Torelli groups
• Automorphisms of surface braid groups
• Superinjective Simplicial Maps of Complexes of Curves and Injective Homomorphisms of Subgroups of Mapping Class Groups II
• Combinatorial rigidity in curve complexes and mapping class groups
• Complexes of Nonseparating Curves and Mapping Class Groups