The CN matrix of a pure braid projection

Fuente: arXiv
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Main Authors: Ozawa, Yuko, Shimizu, Ayaka, Yaguchi, Yoshiro
Format: Preprint
Published: 2025
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author Ozawa, Yuko
Shimizu, Ayaka
Yaguchi, Yoshiro
author_facet Ozawa, Yuko
Shimizu, Ayaka
Yaguchi, Yoshiro
contents The CN matrix of an $n$-braid projection $B$ is an $n \times n$ matrix such that each $(i,j)$ entry indicates the number of crossings between $i^{th}$ and $j^{th}$ strands of $B$. In this paper, several patterns of an $n \times n$ matrix to be a CN matrix are discussed, and the CN matrix of a pure 6-braid projection is characterized. As an application, the OU matrix of a pure 6-braid diagram and the crossing matrix of a positive pure 6-braid are also characterized.
format Preprint
id arxiv_https___arxiv_org_abs_2506_08659
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The CN matrix of a pure braid projection
Ozawa, Yuko
Shimizu, Ayaka
Yaguchi, Yoshiro
Geometric Topology
The CN matrix of an $n$-braid projection $B$ is an $n \times n$ matrix such that each $(i,j)$ entry indicates the number of crossings between $i^{th}$ and $j^{th}$ strands of $B$. In this paper, several patterns of an $n \times n$ matrix to be a CN matrix are discussed, and the CN matrix of a pure 6-braid projection is characterized. As an application, the OU matrix of a pure 6-braid diagram and the crossing matrix of a positive pure 6-braid are also characterized.
title The CN matrix of a pure braid projection
topic Geometric Topology
url https://arxiv.org/abs/2506.08659