An algorithm to calculate generalized Seifert matrices
Stefan Friedl, Chinmaya Kausik, Jos\'e Pedro Quintanilha
TL;DR
This paper introduces an algorithm and software tool for computing generalized Seifert matrices and related link invariants from colored braids, facilitating advanced link analysis.
Contribution
It presents a novel algorithm and implements it in the Clasper program, which computes Seifert matrices, the Conway potential, multivariable Alexander polynomial, and Cimasoni-Florens signatures.
Findings
Successfully computes generalized Seifert matrices for colored links
Outputs multiple link invariants including Alexander polynomial and signatures
Provides visualization of the C-complex structure
Abstract
We develop an algorithm for computing generalized Seifert matrices for colored links given as closures of colored braids. The algorithm has been implemented by the second author as a computer program called Clasper. Clasper also outputs the Conway potential function, the multivariable Alexander polynomial and the Cimasoni-Florens signatures of a link, and displays a visualization of the C-complex used for producing the generalized Seifert matrices.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry