Algebraic and Geometric Topology 1 (2001), paper no. 16, pages 321-347.

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

Oliver T. Dasbach, Brian S. 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

AMS subject classification. Primary: 57M25. Secondary: 57M27, 57M50.

DOI: 10.2140/agt.2001.1.321

E-print: arXiv:math.GT/9911172

Submitted: 14 December 2000. (Revised: 21 May 2001.) Accepted: 25 May 2001. Published: 31 May 2001.

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Oliver T. Dasbach, Brian S. Mangum
University of California, Riverside, Department of Mathematics
Riverside, CA 92521 - 0135, USA
Barnard College/Columbia University, Department of Mathematics
New York, NY 10027, USA
Email: kasten@math.ucr.edu, mangum@math.columbia.edu
URL: http://www.math.ucr.edu/~kasten
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