Work

The crossing matrix and the Burau matrix of pure braids

Year: 2026

Type: preprint

Abstract: 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 from these matrices.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.29147

Authors: Shimizu, Ayaka, Yaguchi, Yoshiro

Institutions: Ochanomizu University, Maebashi Institute of Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

OpenAlex ID: W7204877260

Cites: 5

Cited by:

Related to: 10