Genera and fibredness of Montesinos knots

Mikami Hirasawa and Kunio Murasugi

Vol. 225 (2006), No. 1, 53–83

DOI: 10.2140/pjm.2006.225.53

Abstract

For Montesinos knots, we explicitly construct Seifert surfaces of minimal genus and solve the question of when they are fibred knots. For those of tunnel number one, we show that they are mostly fibred if their Alexander polynomials (of proper degrees) are monic.

Keywords

Seifert surface, fibred knot, Montesinos knot, plumbing, rational tangle, continued fraction, sutured manifold decomposition

Mathematical Subject Classification 2000

Primary: 57M25

Milestones

Received: 19 October 2004

Revised: 31 July 2005

Accepted: 10 August 2005

Published: 1 May 2006