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Matrices and diagrams of cords on a punctured plane

Yoshiro Yaguchi

Department of Mathematics, National Institute of Technology, Gunma College, 580 Toribo-Cho, Maebashi-Shi, Gunma 371-8530, Japan

E-mail Address: yaguchi-y@nat.gunma-ct.ac.jp

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https://doi.org/10.1142/S0218216518500360Cited by:1 (Source: Crossref)

Abstract

A cord is a simple curve on a punctured plane. We introduce diagrams which represent isotopy classes of cords. Using such diagrams, we prove that there is a one-to-one correspondence from the set of the isotopy classes of cords to a set of symmetric matrices whose components are non-negative integers, and we give necessary conditions for matrices to represent the isotopy classes of cords.

Keywords:

AMSC: 57Q35, 57F40

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