Fig. 2: Braid representation of knots.
The diagram of a trefoil knot (a) along with its corresponding braid (b). Both ends of the braid diagram are connected to illustrate how its closure yields the knot in a. A trefoil knot (c) obtained from the stereographic projection of the braid in d. The projection effectively connects both ends of the braid, highlighted by a black outline, thereby transforming the two strands of the braid into a knot and the enclosing cylinder, \({\mathcal{C}}\), into a torus, \({{\mathcal{T}}}_{2}\). e, f An optical-framed knot (e) and its unwrapped form (f) obtained by applying a coordinate transformation on the curve formed by the knot while preserving the local orientation of the knot’s frame. g Extracted twisting angle of the frame of the two strands in the structure shown in f.
