2018/04/30 by Chaim Even-Zohar, Joel Hass, Nati Linial +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CO #math.GT #msc:57M25
paper · pdf · doi:10.1142/s0218216519500317
published as Journal of Knot Theory and Its Ramifications, Vol. 28, No. 07, 1950031 (June 2019)
arxiv created 2018/08/15 · arxiv updated 2019/11/06
We study collections of planar curves that yield diagrams for all knots. In particular, we show that a very special class called potholder curves carries all knots. This has implications for realizing all knots and links as special types of meanders and braids. We also introduce and apply a method to compare the efficiency of various classes of curves that represent all knots.