Finding homotopy group of spheres is an old open problem in topology. Berrick et al. derive in [A. J. Berrick, F. Cohen, Y. L. Wong and J. Wu, Configurations, braids, and homotopy groups, J. Amer. Math. Soc. 19 (2006)] an exact sequence that relates Brunnian braids to homotopy groups of spheres. We give an interpretation of this exact sequence based on the combed form for braids over the sphere developed in [R. Gillette and J. V. Buskirk, The word problem and consequences for the braid groups and mapping class groups of the two-sphere, Trans. Amer. Math. Soc. 131 (1968) 277–296] with the aim of helping one to visualize the sequence and to do calculations based on it.

中文翻译：

---

2 球体上的布伦尼辫子和 Artin 梳理形式

寻找球体的同伦群是拓扑学中一个古老的开放问题。贝里克等。派生于 [AJ Berrick, F. Cohen, YL Wong 和 J. Wu，配置、辫子和同伦群，J.阿米尔。数学。社会党。 19(2006)] 一个精确的序列，将 Brunnian 辫子与球体的同伦群联系起来。我们根据 [R. Gillette 和 JV Buskirk，两个球体的编织组和映射类组的单词问题和后果，反式。阿米尔。数学。社会党。 131(1968) 277–296] 旨在帮助人们可视化序列并基于它进行计算。