Rewriting systems in alternating knot groups with the Dehn presentation

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.