Rewriting Systems in Alternating Knot groups with the Dehn presentation

Details Rewriting Systems in Alternating Knot groups with the Dehn presentation Rewriting Systems in Alternating Knot groups with the Dehn presentation

2008-04-08

arxiv.org/abs/0804.1200v1

Geom. Dedicata 138 (2009), 173-192

Mathematics

Group Theory

Scientific paper

10.1007/s10711-008-9306-5

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.

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