Tied pseudo links \& pseudo knotoids (Q821506)

In this paper the author studies generalizations of knot- and braid-diagrams with their modified versions of Reidemeister- and braiding-moves. Such generalizations are the following: Pseudo knot diagrams (and pseudo braid diagrams), which are diagrams with some missing crossing information, that is, for some crossings, it is unknown which strand passes over and which strand passes under the other. Tied Pseudo links (and tied pseudo braids) where components (or strands of the braid) are tied, where the ties are represented by extra arcs in a diagram. The author formulates and proves analogues of the Alexander and Markov theorems for tied pseudo links. Finally, the author introduces the theory of pseudo knotoids, that generalizes the notion of knotoids. The braid analog of a knotoid is called a braidoid. The author states (and proves) the analogues of the Alexander and Markov theorems for pseudo knotoids. This can be further generalized to tied (multi)-knotoids and tied pseudo (multi)-knotoids. The author notes that the theory of pseudo knots has been proposed as a tool to study open-knotted protein chains in molecular biology.