Computation of Gordian distances and H2-Gordian distances of knots

Abstract

In this paper we discuss the possibility of computing unknotting number from minimal knot diagrams, Bernhard-Jablan Conjecture, unknown knot distances between non-rational knots and of searching minimal distances by using a graph with weighted edges representing knot distances. Since topoizomerazes are enzymes involved in changing crossing of DNA, knot distances can be used to study topoizomerazes actions. We compute some undecided knot distances 1 known from the literature, and extend the computations by computing knots with smoothing number one with at most n = 11 crossings and smoothing knot distances of knots with at most n = 9 crossings. All computations are done in the program LinKnot, based on Conway notation and nonminimal representations of knots.