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

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

1999-11-23

arxiv.org/abs/math/9911172v2

Algebr. Geom. Topol. 1 (2001) 321-347

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-16.abs.html

Scientific paper

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.

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