Connectivity Properties of Factorization Posets in Generated Groups

被引：0
作者：
Henri Mühle
Vivien Ripoll
机构：
[1] Technische Universität Dresden,Institut für Algebra
[2] Universität Wien,Fakultät für Mathematik
来源：
Order | 2020年 / 37卷
关键词：
Generated group; Braid group; Hurwitz action; Factorization poset; Shellability; Compatible order; Well-covered poset; Cycle graph; Noncrossing partition lattice;
D O I：
暂无
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学科分类号：
摘要：
We consider three notions of connectivity and their interactions in partially ordered sets coming from reduced factorizations of an element in a generated group. While one form of connectivity essentially reflects the connectivity of the poset diagram, the other two are a bit more involved: Hurwitz-connectivity has its origins in algebraic geometry, and shellability in topology. We propose a framework to study these connectivity properties in a uniform way. Our main tool is a certain linear order of the generators that is compatible with the chosen element.
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页码：115 / 149
页数：34
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