Automorphic sets and braids and singularities
Automorphic sets and braids and singularities
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自守集、辫子和奇点
DOI：
10.1090/conm/078/975077
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发表时间：
1988
影响因子：
1.3
通讯作者：
E. Brieskorn
中科院分区：
文献类型：
--
作者：
E. Brieskorn
引言奇异点和辫子在很多方面都有联系。我决定集中讨论这些关系的一个方面，即考克斯特图。这些都是不变量的奇点，这是由经典理论的皮卡德和莱夫谢茨。辫子群Bn操作的一组图与n个顶点，和不变量相关联的奇异性是一个轨道的diagrams.When准备这项调查，我发现了一个非常简单的概念，统一了许多调查这个问题以及经典的结果E。Artin和A. Hurwitz和W.马格纳斯这就是自守集的概念。一个自同构集是一个集合▲，它的乘积使得所有的左平移B→ ab都是自同构。如果▲是一个自守集，则对任意自然数n，存在辫子群B在上的一个标准运算。n
INTRODUCTION Singularities and braids are related in many ways. I decided to concentrate on one aspect of these relations, namely the Coxeter diagrams. These are invariants of singularities which are obtained by the classical theory of Picard and Lefschetz. The braid groups Bn operate on the set of diagrams with n vertices, and the invariant associated to a singularity is an orbit of diagrams.When preparing this survey, I found an extremely simple concept unifying many investigations on this subject as well as classical results of E. Artin and A. Hurwitz and W. Magnus. This is the notion of an automorphic set. An automorphic set is a set▲ with a product such that all left translations b→ ab are automorphisms. If▲ is an automorphic set, there is a canonical operation of the braid group B on for any natural number n. n