The knots that lie above all shadows

Abstract

We show that for each even integer m ≥ 2, every reduced shadow with sufficiently many crossings is a shadow of a torus knot T 2,m+1 , or of a twist knot Tm, or of a connected sum of m trefoil knots.

A bracket polynomial for 2-tangle shadows

“…A 2-tangle shadow is a 2-tangle diagram without under/over crossing information [Kre99,MS19]. The following definition holds for such class of tangles.…”