辫子、偏序集和正交概型
Braids, posets and orthoschemes
摘要：
在这篇文章中，我们研究了分次偏序集的序复形在一个度量下的曲率性质，我们称之为“正交方案度量”。除了其他的结果，我们刻画了哪些秩4偏序集有CAT（0）正交方案复形，并通过将这个定理应用于标准偏序集和与四生成元Artin群相关的复形，我们能够证明5-弦辫群是紧致非正曲空间的基本群。
英文摘要：
In this article we study the curvature properties of the order complex of a graded poset under a metric that we call the ``orthoscheme metric''. In addition to other results, we characterize which rank 4 posets have CAT(0) orthoscheme complexes and by applying this theorem to standard posets and complexes associated with four-generator Artin groups, we are able to show that the 5-string braid group is the fundamental group of a compact nonpositively curved space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
