Document Type
Article - post-print
Publication Date
2012
Abstract
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.
Digital Commons @ LMU & LLS Citation
Garrabrant, Scott M., Jim Hoste and Patrick D. Shanahan. "Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots." Journal of Knot Theory and its Ramifications, Vol. 21, No. 9 (2012) 1-24. arXiv:1007.3278
Comments
This is a post-print version of the article.