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

Dasbach, Oliver T¹ ; Mangum, Brian S²

¹University of California, Riverside, Department of Mathematics, Riverside CA 92521-0135, USA
²Barnard College, Columbia University, Department of Mathematics, New York NY 10027, USA

Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 321-347

Résumé

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.

Détail

DOI : 10.2140/agt.2001.1.321

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

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