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Unknotting operations on knots and links
Journal of Knot Theory and Its Ramifications ( IF 0.3 ) Pub Date : 2021-03-13 , DOI: 10.1142/s0218216521710012
Ayaka Shimizu 1
Affiliation  

By considering unknotting operations, we obtain ways of measuring how knotted a knot is. Unknotting phenomena can be seen not only in knot theory, but also in various settings such as DNA knots, mind knots and so on ([C. C. Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (American Mathematical Society, Providence, RI, 2004); A. Kawauchi, K. Kishimoto and A. Shimizu, Knot theory and game (in Japanese) (Asakura Publishing, Tokyo, 2013); L. Rudolph, Qualitative Mathematics for the Social Sciences (Routledge, London, 2013); K. Murasugi, Knot Theory and Its Applications, Translated from the 1993 Japanese original by Bohdan Kupita (Birkhauser, Boston, MA, 1996)], etc.). In this paper, we see how knots can be unknotted (and therefore how they are knotted) by considering various unknotting operations and their associated unknotting numbers.

中文翻译:

对结和链接进行解结操作

通过考虑解结操作,我们获得了测量结的打结程度的方法。解结现象不仅可以在结理论中看到,还可以在 DNA 结、心灵结等各种设置中看到([C. C. Adams,结书:结的数学理论入门(美国数学会,普罗维登斯,罗德岛州,2004 年);A. Kawauchi、K. Kishimoto 和 A. Shimizu,结理论与博弈(日文)(朝仓出版社,东京,2013 年);L.鲁道夫,社会科学的定性数学(劳特利奇,伦敦,2013 年);K.村杉,结理论及其应用, 翻译自 Bohdan Kupita (Birkhauser, Boston, MA, 1996)] 等的 1993 年日文原版。在本文中,我们通过考虑各种解开操作及其相关的解开数来了解如何解开结(以及如何打结)。
更新日期:2021-03-13
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