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Unique diagram of a spatial arc and the knotting probability

2019/07/24 by Akio Kawauchi, Kawauchi, Akio
Computer Science · Mathematics · #57M25 #57Q45 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1907.10194

openalex publication_date 2019/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the projection image of an oriented spatial arc to any oriented plane is approximated by a unique arc diagram (up to isomorphic arc diagrams) determined from the spatial arc and the projection. In a separated paper, the knotting probability of an arc diagram is defined as an invariant under isomorphic arc diagrams. By combining them, the knotting probability of every oriented spatial arc is defined.

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