Algorithmic Invariants for Alexander Modules
- 437 Downloads
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.
Unable to display preview. Download preview PDF.
- [Adams et al.(1994)]
- [Burde et al.(1985)]
- [Crowell et al.(1977)]
- [Fox et al.(1964)]
- [Kearton et al.(2003)]
- [Lickorish(1998)]Lickorish, W.B.R.: An introduction to knot theory. Graduate Texts in Mathematics, vol. 175. Springer, New York (1998)Google Scholar
- [Livingston(2004)]Livingston, C.: Table of knot invariants, At: http://www.indiana.edu/~knotinfo/
- [Pauer et al.(1999)]