Fibred torti-rational knots
Geometric Topology
2008-10-23 v1
Abstract
A torti-rational knot, denoted by K(2a,b|r), is a knot obtained from the 2-bridge link B(2a,b) by applying Dehn twists an arbitrary number of times, r, along one component of B(2a,b). We determine the genus of K(2a,b|r) and solve a question of when K(2a,b|r) is fibred. In most cases, the Alexander polynomials determine the genus and fibredness of these knots. We develop both algebraic and geometric techniques to describe the genus and fibredness by means of continued fraction expansions of b/2a. Then, we explicitly construct minimal genus Seifert surfaces. As an application, we solve the same question for the satellite knots of tunnel number one.
Keywords
Cite
@article{arxiv.0810.4044,
title = {Fibred torti-rational knots},
author = {M. Hirasawa and K. Murasugi},
journal= {arXiv preprint arXiv:0810.4044},
year = {2008}
}