Brunnian braids over the 2-sphere and Artin combed form

• Main Authors: Duzhin, Fedor, Jessica, Loh Sher En
• 其他作者: School of Physical and Mathematical Sciences
• 格式: Article
• 語言: English
• 出版: 2022
• 主題: Braid Groups; Homotopy Groups of Spheres
• 在線閱讀: https://hdl.handle.net/10356/160042

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.