Chapter of Book
Algorithmic Invariants for Alexander Modules
Author/s | Gago Vargas, Manuel Jesús
Hartillo Hermoso, Isabel Ucha Enríquez, José María |
Department | Universidad de Sevilla. Departamento de Álgebra |
Publication Date | 2006 |
Deposit Date | 2015-03-27 |
Published in |
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ISBN/ISSN | 978-3-540-45182-2 |
Abstract | Let $G$ be a group given by generators and relations. It is
possible to compute a presentation matrix of a module over a ring
through Fox's differential calculus. We show how to use Gröbner
bases as an algorithmic tool ... Let $G$ be a group given by generators and relations. It is possible to compute a presentation matrix of a module over a ring through Fox's differential calculus. We show how to use Gröbner bases as an algorithmic tool to compare the chains of elementary ideals defined by the matrix. We apply this technique to classical examples of groups and to compute the elementary ideals of Alexander matrix of knots up to $11$ crossings with the same Alexander polynomial. |
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grobner-knots-ams.pdf | 244.0Kb | [PDF] | View/ | |