发表机构
Department of Mathematics, Graduate School of Science, Kyoto University（京都大学理学研究科数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广Milnor不等式至纽结类的$C^1$-闭包，结合近期工作解决圆形弹性纽结猜想，证明当桥指数与辫指数相同时，多重覆盖圆为唯一弹性纽结。
AI 中文摘要
我们建立了Milnor不等式的推广，将总曲率与桥指数联系起来，推广到纽结类的$C^1$-闭包，对极限曲线的自交点没有任何限制。结合Reiter–von der Mosel的近期工作，这解决了圆形弹性纽结猜想，该猜想最初由Gallotti–Pierre-Louis于2007年预测，随后由Gerlach–Reiter–von der Mosel于2017年表述为数学猜想。更精确地说，如果某个 tame 纽结类的桥指数与辫指数一致，那么多重覆盖圆是唯一的弹性纽结。
英文摘要
We establish the extension of Milnor's inequality, relating total curvature with the bridge index, to the $C^1$-closure of a knot class, without any restriction on the self-intersections of the limit curve. Together with recent work of Reiter--von der Mosel, this resolves the circular elastic knot conjecture, first predicted by Gallotti--Pierre-Louis in 2007 and then formulated as a mathematical conjecture by Gerlach--Reiter--von der Mosel in 2017. More precisely, if the bridge and braid indices of a tame knot class coincide, then the multiply covered circle is the unique elastic knot.
Comments14 pages
