Constructing Goeritz matrix from Dehn coloring matrix
Geometric Topology
2022-11-23 v2
Abstract
Associated to a knot diagram, Goeritz introduced an integral matrix, which is now called a Goeritz matrix. It was shown by Traldi that the solution space of the equations with Goeritz matrix (precisely, unreduced Goeritz matrix called in his paper) as a coefficient matrix is isomorphic to the linear space consisting of the Dehn colorings for a knot. In this paper, we give a construction of a Goeritz matrix from a Dehn coloring matrix, from which Dehn colorings are induced. Moreover, if the knot diagram is prime, we give a purely algebraic construction of a Goeritz matrix from a Dehn coloring matrix.
Cite
@article{arxiv.2206.01983,
title = {Constructing Goeritz matrix from Dehn coloring matrix},
author = {Masaki Horiuchi and Kazuhiro Ichihara and Eri Matsudo and Sota Yoshida},
journal= {arXiv preprint arXiv:2206.01983},
year = {2022}
}
Comments
10 pages, 6 figures