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arXiv · 2608.13789

The crossing numbers of knots and links via 4D topology

Akio Kawauchi
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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.

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Akio Kawauchi. 2026-08-13. The crossing numbers of knots and links via 4D topology. https://arxiv.org/abs/2608.13789

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