论文标题
绑定伪链接\＆伪旋转
Tied pseudo links \& Pseudo knotoids
论文作者
论文摘要
在本文中，我们研究了{\ it伪结}的理论，该理论是带有一些缺失的交叉信息的结，我们介绍和研究{\ it pseudo绑定链接}的理论和{\ it pseudo knotoids}的理论。特别是，我们首先提出了一种用于伪结的编织算法，然后在该环境中介绍了$ l $ - moves，使用该算法，我们制定了Markov Theorem的伪造辫子的模拟版本。然后，我们介绍并研究了{\ IT绑定的伪链接}的理论，该理论概括了绑定链接的概念，我们利用了绑定的伪链接和绑定的奇异链接之间的关系。我们首先提出了绑架单数辫子的$ l $ move编织物。然后，我们介绍了绑定的伪编织单型单体，我们为绑定的伪链路制定并证明了亚历山大和马尔可夫定理的类似物。最后，我们介绍并研究了{\ it伪结节}的理论，这些理论概括了结节的概念。我们提出了伪结节的同位素定理，然后将其传递到辫子的水平。我们通过介绍{\ it pseudo} $ l $ {\ it -moves}并介绍Alexander和Markov定理的伪定义来进一步介绍和研究{\ it伪辫子}。我们还讨论了与{\ it（多） - 结和绑定的伪（多） - 结s}有关的进一步研究。伪结理论可以作为DNA研究的强大工具，而绑定的链接在分子生物学的其他方面具有潜在的用途。
In this paper we study the theory of {\it pseudo knots}, which are knots with some missing crossing information, and we introduce and study the theory of {\it pseudo tied links} and the theory of {\it pseudo knotoids}. In particular, we first present a braiding algorithm for pseudo knots and we then introduce the $L$-moves in that setting, with the use of which we formulate a sharpened version of the analogue of the Markov theorem for pseudo braids. Then we introduce and study the theory of {\it tied pseudo links}, that generalize the notion of tied links, and we exploit the relation between tied pseudo links and tied singular links. We first present an $L$-move braid equivalence for tied singular braids. Then, we introduce the tied pseudo braid monoid and we formulate and prove analogues of the Alexander and Markov theorems for tied pseudo links. Finally, we introduce and study the theory of {\it pseudo knotoids}, that generalize the notion of knotoids. We present an isotopy theorem for pseudo knotoids and we then pass to the level of braidoids. We further introduce and study the {\it pseudo braidoids} by introducing the {\it pseudo} $L${\it -moves} and by presenting the analogues of the Alexander and Markov theorems for pseudo knotoids. We also discuss further research related to {\it tied (multi)-knotoids and tied pseudo (multi)-knotoids}. The theory of pseudo knots may serve as a strong tool in the study of DNA, while tied links have potential use in other aspects of molecular biology.
