标题： 连续非交叉分划与加权循环分解 显示英文标题

标题： Continuous Noncrossing Partitions and Weighted Circular Factorizations

摘要： 本文研究复平面上单位圆的非交叉划分；我们称这些为连续非交叉划分。 更准确地说，我们关注度为$d$的连续非交叉划分，其中同一块中的单位复数具有相同的$d$次幂。 我们证明，度为$d$的连续非交叉划分为一个拓扑偏序集，其不可数的元素集合可以通过我们称之为$d$-循环因子的加权线性分解对象的等价类进行索引。 此外，该偏序集中的极大元素形成一个与$d$-弦辫群的对偶 Garside 分类空间同胚的子空间。 单位圆的度为$d$的连续非交叉划分是更一般构造的一个特例。 对于任何 Coxeter 群 $W$中的 Coxeter 元素 $c$的每个选择，我们定义一个拓扑偏序集，它是 $c$在 $W$中的因子的加权线性分解的等价类，我们将该偏序集中的元素称为连续 $c$-非交叉划分。 此偏序集中的极大元素形成一个与单顶点复形同胚的子空间，其基本群是相应的对偶 Artin 群。 显示英文摘要

摘要： This article examines noncrossing partitions of the unit circle in the complex plane; we call these continuous noncrossing partitions. More precisely, we focus on the degree-$d$ continuous noncrossing partitions where unit complex numbers in the same block have identical $d$-th powers. We prove that the degree-$d$ continuous noncrossing partitions form a topological poset whose uncountable set of elements can be indexed by equivalence classes of objects we call weighted linear factorizations of factors of a $d$-cycle. Moreover, the maximal elements in this poset form a subspace homeomorphic to the dual Garside classifying space for the $d$-strand braid group. The degree-$d$ continuous noncrossing partitions of the unit circle are a special case of a more general construction. For every choice of Coxeter element $c$ in any Coxeter group $W$ we define a topological poset of equivalence classes of weighted linear factorizations of factors of $c$ in $W$ whose elements we call continuous $c$-noncrossing partitions. The maximal elements in this poset form a subspace homeomorphic to the one-vertex complex whose fundamental group is the corresponding dual Artin group.