On the Harary-Kauffman Conjecture and Turk's Head Knots
Geometric Topology
2008-11-04 v1
Abstract
The m,n Turk's Head Knot, THK(m,n), is an "alternating (m,n) torus knot." We prove the Harary-Kauffman conjecture for all THK(m,n) except for the case where m \geq 5 is odd and n \geq 3 is relatively prime to m. We also give evidence in support of the conjecture in that case. Our proof rests on the observation that none of these knots have prime determinant except for THK(m,2) when P_m is a Pell prime.
Keywords
Cite
@article{arxiv.0811.0044,
title = {On the Harary-Kauffman Conjecture and Turk's Head Knots},
author = {Nicholas E. Dowdall and Thomas W. Mattman and Kevin Meek and Pablo R. Solis},
journal= {arXiv preprint arXiv:0811.0044},
year = {2008}
}
Comments
16 pages, 12 figures