Goeritz and Seifert Matrices from Dehn Presentations
Daniel S. Silver, Lorenzo Traldi, Susan G. Williams
TL;DR
This paper explores how to derive the Goeritz and Seifert matrices of a link directly from Dehn presentations using Fox calculus, providing a new algebraic approach to link invariants.
Contribution
It introduces a method to compute Goeritz and Seifert matrices from Dehn presentations, linking algebraic and topological link invariants.
Findings
Goeritz matrix obtained from Jacobian of Dehn presentation
Seifert matrix derived for special diagrams
Provides algebraic tools for link invariant computation
Abstract
The Goeritz matrix of a link is obtained from the Jacobian matrix of a modified Dehn presentation associated to a diagram using Fox's free differential calculus. When the diagram is special the Seifert matrix can also be determined from the presentation.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models