Non-trivialization probability of arc system in three-dimensional space

Akio Kawauchi

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arXiv · 2606.22024

Non-trivialization probability of arc system in three-dimensional space

Akio Kawauchi

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Abstract

The type-specific knotting probability of an arc diagram is earlier defined by using chord diagrams of ribbon surface-links in 4D space. By modifying this notion, Non-Trivialization probability (simply NT probability) for the arc diagram is introduced and generalized to an arc system diagram. Some properties of the NT probability are shown. The method of transforming a polygonal arc in 3D space into a unique arc diagram up to isomorphisms earlier developed is generalized to a polygonal arc system in 3D space to define the NT probability.

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Akio Kawauchi. 2026-06-20. Non-trivialization probability of arc system in three-dimensional space. https://arxiv.org/abs/2606.22024

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