On the warping sum of knots

Abstract

The warping sum $e(K)$ of a knot $K$ is the minimal value of the sum of the warping degrees of a minimal diagram of $K$ with both orientations. In this paper, knots $K$ with $e(K)\le 3$ are characterized, and some knots $K$ with $e(K)=4$ are given.

10 pages, 6 figures, to appear in JKTR Special Issue on "Self-distributive system and quandle (co)homology theory in algebra and low-dimensional topology, 2017 KIAS Research Station"