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Title: Brunnian braids over the 2-sphere and Artin combed form
Authors: Duzhin, Fedor
Loh, Jessica Sher En
Keywords: Science::Mathematics
Issue Date: 2021
Source: Duzhin, F. & Loh, J. S. E. (2021). Brunnian braids over the 2-sphere and Artin combed form. Journal of Knot Theory and Its Ramifications, 30(3), 2150012-1-2150012-9.
Journal: Journal of Knot Theory and Its Ramifications
Abstract: 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.
ISSN: 0218-2165
DOI: 10.1142/S0218216521500127
Schools: School of Physical and Mathematical Sciences 
School of Computer Science and Engineering 
Rights: © World Scientific Publishing Company. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SCSE Journal Articles
SPMS Journal Articles

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