On McMullen's and other inequalities for the 
Thurston norm of link complements

Algebraic and Geometric Topology, Volume 1 (2001), pages 321-347

Preprint available: arXiv:math/9911172
MathSciNet Review

Oliver T. Dasbach, Brian Mangum

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