Ayaka Shimizu

activity

20242026

collaborators

9 papers

math.GT2026

The crossing matrix and the Burau matrix of pure braids

Ayaka Shimizu, Yoshiro Yaguchi

We show that the first derivative of the Burau matrix at $t = 1$ coincides with the Laplacian of the crossing matrix for pure braids. We also discuss conjugacy invariants derived fro…

math.GT2026

Cabled braids and their crossing matrices

Ayaka Shimizu, Yoshiro Yaguchi

We study cabling operations on braids, and characterize the matrices that can be realized as crossing matrices of reducible pure braids. We also use cabling to construct enhanced c…

math.GT2026

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence

Ayaka Shimizu, Yoshiro Yaguchi

We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surfac…

math.GT2025

Determinant of the crossing matrix of a braid

Ayaka Shimizu

In this paper, we define a braid invariant, the purified determinant $P (b)$ of a braid $b$ , considering the determinant of the crossing matrix of a pure braid derived from $b$ , and…

math.GT2025

The CN matrix of a pure braid projection

Yuko Ozawa, Ayaka Shimizu, Yoshiro Yaguchi

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 $i^{t h}$ and $j^{t h}$ strands of $B$ .…

math.GT2025

Characterization of the OU matrix of a braid diagram

Ayaka Shimizu, Yoshiro Yaguchi

The OU matrix of a braid diagram is a square matrix that represents the number of over/under crossings of each pair of strands. In this paper, the OU matrix of a pure braid diagram…

math.GT2024

Orbits by the up-down action of braid diagrams

Komal Negi, Ayaka Shimizu, Yoshiro Yaguchi +1

The set of all virtual or classical braid diagrams forms a monoid and gives a natural monoid action on a direct product of $Z$ called the up-down action. In this paper, w…

math.GT2024

Determinant of the OU matrix of a braid diagram

Ayaka Shimizu, Yoshiro Yaguchi

In this paper, we define the OU matrix of a braid diagram and discuss how the OU matrix reflects the warping degree or the layeredness of the braid diagram, and show that the deter…

math.GT2024

Warping labeling for twisted knots and twisted virtual braids

Komal Negi, Ayaka Shimizu, Madeti Prabhakar

In this paper, we introduce the concept of the warping degree for twisted knots, construct an invariant for them, and utilize it to establish a labeling scheme for these knots, kno…