Algebraic & Geometric Topology 1 (2001) 321–347

DOI: 10.2140/agt.2001.1.321

arXiv: math.GT/9911172

Abstract

In a recent paper, McMullen showed an inequality between the Thurston norm and the Alexander norm of a 3–manifold. This generalizes the well-known fact that twice the genus of a knot is bounded from below by the degree of the Alexander polynomial.

We extend the Bennequin inequality for links to an inequality for all points of the Thurston norm, if the manifold is a link complement. We compare these two inequalities on two classes of closed braids.

In an additional section we discuss a conjectured inequality due to Morton for certain points of the Thurston norm. We prove Morton’s conjecture for closed 3–braids.

Keywords

Thurston norm, Alexander norm, multivariable Alexander polynomial, fibred links, positive braids, Bennequin's inequality, Bennequin surface, Morton's conjecture

Mathematical Subject Classification

Primary: 57M25

Secondary: 57M27, 57M50

References

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Publication

Received: 14 December 2000
Revised: 21 May 2001
Accepted: 25 May 2001
Published: 31 May 2001

Authors