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

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 i...

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Veröffentlicht in:arXiv.org 2001-06
Hauptverfasser: Dasbach, Oliver T, Mangum, Brian S
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Braiding
Inequalities
Inequality
Manifolds
Polynomials
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description 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.
doi_str_mv 10.48550/arxiv.9911172
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subjects Braiding
Inequalities
Inequality
Manifolds
Polynomials
title On McMullen's and other inequalities for the Thurston norm of link complements
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