The twisting number of a ribbon knot is bounded below by its doubly slice genus

2024/04/11 by Brejevs, Vitalijs, Feller, Peter
#57K10 #57K30 #57K40 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2404.07619

Abstract

The twisting number of a ribbon knot K is the minimal number of tangle replacements on the symmetry axis of J # -J for any knot J that is required to produce a symmetric union diagram of K. We prove that the twisting number is bounded below by the doubly slice genus and produce examples of ribbon knots with arbitrarily high twisting number, addressing a problem of Tanaka. As an application, we determine hitherto unknown doubly slice genera of some knots with 12 crossings.

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