矩形图的括号。琼斯猜想的证明及相关问题
Bypasses for rectangular diagrams. Proof of Jones' conjecture and related questions
摘要：
本文用勒让德结给出了矩形图允许化简的一个判据。它表明，有两种类型的简化是相互独立的意义。给出了非纽结的单调化简定理的一个新证明。它示出了一个最小的矩形图最大化相应的Legendrian链接的Thurston-Bennequin数。证明了Jones关于表示固定链环类型的最小辫的交点的代数数不变性的猜想。
英文摘要：
In the present paper a criteria for a rectangular diagram to admit a simplification is given in terms of Legendrian knots. It is shown that there are two types of simplifications which are mutually independent in a sense. A new proof of the monotonic simplification theorem for the unknot is given. It is shown that a minimal rectangular diagram maximizes the Thurston--Bennequin number for the corresponding Legendrian links. Jones' conjecture about the invariance of the algebraic number of intersections of a minimal braid representing a fixed link type is proved.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
