Rewriting Systems in Alternating Knot groups with the Dehn presentation
Group Theory
2011-02-01 v1
Abstract
Every tame, prime and alternating knot is equivalent to a tame, prime and alternating knot in regular position, with a common projection. In this work, we show that the Dehn presentation of the knot group of a tame, prime, alternating knot, with a regular and common projection has a finite and complete rewriting system. Although there are rules in the rewriting system with left-hand side a generator and which increase the length of the words we show that the system is terminating.
Cite
@article{arxiv.0804.1200,
title = {Rewriting Systems in Alternating Knot groups with the Dehn presentation},
author = {Fabienne Chouraqui},
journal= {arXiv preprint arXiv:0804.1200},
year = {2011}
}