Braidoids

Knotoids, pseudo knotoids, Braidoids and pseudo braidoids on the Torus

In this paper we study the theory of knotoids and braidoids and the theory of pseudo knotoids and pseudo braidoids on the torus T. In particular, we introduce the notion of {\it mixed knotoids} in $S^2$, that generalize the notion of mixed links in $S^3$, and we present an isotopy theorem for mixed knotoids. We then generalize the Kauffman bracket polynomial, $<;>$, for mixed knotoids and we present a state sum formula for $<;>$. We also introduce the notion of {\it mixed pseudo knotoids}, that is, multi-knotoids on two components with some missing crossing information. More precisely, we pres…

球面纽结类的辫状等价性

A braidoid equivalence for spherical knotoids

本研究针对球面纽结类的辫状表示问题，通过细化辫状图的L-等价概念，建立了S²中（多）纽结类图以带标记辫状图闭包表示时的等价定理，完善了辫状理论与纽结类理论的对应关系。

A survey on knotoids, braidoids and their applications

This paper is a survey on the theory of knotoids and braidoids. Knotoids are open ended knot diagrams in surfaces and braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids in the plane. We survey through the fundamental notions and existing works on these objects as well as their applications in the study of proteins.

Tied pseudo links \& Pseudo knotoids

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 t…