Laces: a generalisation of braids (Q5939255)

One of the standard correspondences between braids and homeomorphisms of punctured discs allows braids on \(n\) strings to be represented by \(n\) disjoint arcs embedded in the plane, under suitable restrictions. In this paper the authors consider general planar embeddings of \(n\) disjoint arcs with fixed endpoints, which they call `laces'. They go on to discuss their relation with \(n\)-braids and with \(n\)-bridge knots, using appropriate constructions and notions of equivalence.