Hyperbolicity of 3-trip Lorenz knots

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• 作者：Jiming Ma¹ ; ^{majiming@fudan.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：57M50 ; 20F36 ; 37C10 ; 57M25
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：212
• 期：Complete
• 页码：57-70
• 全文大小：437 K

文摘

Using Xu's conjugacy algorithm on the braid group B₃$B_3$ and  and the hyperbolicity criterion of 3-braid links by Futer–Kalfagianni–Purcell [14], we classify Lorenz knots of trip number 3 into torus knots and hyperbolic knots.

Moreover, we provide another approach to this problem. Modulo a conjectural pseudo-Anosov criterion, we can also classify Lorenz knots of trip number 3 based upon the Dehornoy floor theory. The author believes that the second approach is promising for the hyperbolicity of more classes of Lorenz knots.