Injections of Artin groups | Zendy

Robert W. Bell | Zendy; Dan Margalit | Zendy

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Injections of Artin groups

Author(s) -

Robert W. Bell,

Dan Margalit

Publication year - 2007

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/108

Subject(s) - mathematics , homeomorphism (graph theory) , injective function , homomorphism , braid group , modulo , outer automorphism group , group (periodic table) , automorphism , pure mathematics , mapping class group , combinatorics , artin group , automorphism group , surface (topology) , coxeter group , geometry , chemistry , organic chemistry

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.

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