Mathematics > Geometric Topology
[Submitted on 26 Apr 2018 (v1), last revised 15 Aug 2018 (this version, v4)]
Title:Universal Knot Diagrams
View PDFAbstract: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.
Submission history
From: Chaim Even-Zohar [view email][v1] Thu, 26 Apr 2018 02:31:01 UTC (32 KB)
[v2] Mon, 4 Jun 2018 05:00:32 UTC (33 KB)
[v3] Wed, 1 Aug 2018 21:12:59 UTC (33 KB)
[v4] Wed, 15 Aug 2018 22:15:16 UTC (33 KB)
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