Injections of Artin Groups
نویسندگان
چکیده
We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a punctured sphere. In particular, we show that any injective homomorphism between these groups is parameterized by a homeomorphism of a punctured disk together with a homomorphism to the integers. 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.
منابع مشابه
ar X iv : m at h / 05 01 05 1 v 1 [ m at h . G R ] 4 J an 2 00 5 INJECTIONS OF ARTIN GROUPS
We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a punctured sphere. In particular, we show that any injective homomorphism between these groups is parameterized by a homeomorphism of a punctured disk together with a homomorphism to the integers. The technique, following Ivanov, is to prove that every superinjective map of the com...
متن کاملar X iv : m at h / 05 01 05 1 v 2 [ m at h . G R ] 1 7 M ay 2 00 6 INJECTIONS OF ARTIN GROUPS
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 g...
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