Flowlines transverse to knot and link fibrations

Robert Ghrist and Eiko Kin

Vol. 217 (2004), No. 1, 61–86

DOI: 10.2140/pjm.2004.217.61

Abstract

A knot or link in S³ is fibred if the complement fibres over S¹, the fibres being spanning surfaces. We focus on those fibred knots and links which have the following property: every vector field transverse to the fibres possesses closed flow lines of all possible knot and link types in S³. Our main result is that a large class of fibred knots and links has this property, including all fibred nontorus 2-bridge knots. In general, sufficient conditions include a pseudo-Anosov type monodromy map and a sufficiently high degree of symmetry.

Milestones

Received: 1 July 2003

Revised: 7 November 2003

Published: 1 November 2004