Link mutations and Goeritz matrices

TL;DR

This paper proves that the mutation class of a classical link can be uniquely identified by its associated Goeritz matrices, extending previous theorems in knot theory.

Contribution

It establishes that Goeritz matrices fully determine the mutation class of classical links, generalizing earlier results by Greene and Lipson.

Findings

Goeritz matrices determine link mutation classes

Extension of Greene's and Lipson's theorems

Provides a new method for classifying links

Abstract

Extending theorems of J. E. Greene [Invent. Math. 192 (2013), 717-750] and A. S. Lipson [Enseign. Math. (2) 36 (1990), 93-114], we prove that the equivalence class of a classical link L under mutation is determined by Goeritz matrices associated to diagrams of L.