The crossing numbers of knots and links via 4D topology

Abstract

The diagrams of links (including knots) are characterized in terms of circular rigid disk-chord diagrams of their spun ribbon torus-links in the 4-sphere. As a result, the crossing numbers of links are equal to the chord indexes of their spun ribbon torus-links. By using this result, additivity on the crossing numbers of links under connected sums can be shown.