arXiv subjects
Publications and source records attributed to Anastasios Kokkinakis.
We introduce framed versions of the $L$-moves and prove a one move theorem for the extension of the Markov theorem for framed braids. We further introduce framed versions of the Hilden and Pure Hilden groups, we give presentations and we use them to state and prove a framed version of the Birman theorem for framed links in plat representation.
Braidoids form a counterpart theory to the theory of planar knotoids, just as braids do for three-dimensional links. As such, planar knotoid diagrams represent the same knotoid in $\mathbb{R}^2$ if and only if they can be presented as the closure of two labeled braidoid diagrams related by an equivalence relation, named $L$-equivalence. In this paper, we refine the notion of $L$-equivalence of braidoid diagrams in order to obtain an equivalence theorem for (multi)-knotoid diagrams in $S^2$ when represented as the closure of labeled braidoid diagrams.