Injections of Artin groups
Injections of Artin groups
复制标题
Artin组注射
DOI：
--
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
D. Margalit
中科院分区：
文献类型：
--
作者：
Robert W. Bell;D. Margalit
我们研究那些 Artin 群，这些 Artin 群以其中心为模，是具有至少 5 个穿孔的球体的映射类群的有限索引子群。特别是，我们证明这些群之间的任何单射同态都是由穿孔球体的同态和整数映射给出的。遵循伊万诺夫的技术是为了证明具有至少 5 个穿孔的球体曲线复形的每个超射图都是由同胚诱导的。我们还确定了至少 4 条纯辫子群的自同构群。
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.