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
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