Injections of Artin groups

By Robert W. Bell, Dany Margalit. 2005

50 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/93535c4fa053c7499571107fa262ef34a1172404

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

COMBINATORIAL RIGIDITY IN CURVE COMPLEXES AND MAPPING CLASS GROUPS (2005, methodology): “This is now a well-established strategy on which we have nothing to add, and a thorough account can be found in both [Bell and Margalit 2005] and [Irmak 2004b].”
Curve Complexes and Finite Index Subgroups of Mapping Class Groups (2005, background): “When, in the conclusion of the proposition, is trivial, we remark that ρ is a transvection in a sense slightly generalizing that of Charney–Crisp [8] (see also [ 3 ] [24]).”