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2001 On McMullen's and other inequalities for the Thurston norm of link complements
Oliver T Dasbach, Brian S Mangum
Algebr. Geom. Topol. 1(1): 321-347 (2001). DOI: 10.2140/agt.2001.1.321

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.

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Oliver T Dasbach. Brian S Mangum. "On McMullen's and other inequalities for the Thurston norm of link complements." Algebr. Geom. Topol. 1 (1) 321 - 347, 2001. https://doi.org/10.2140/agt.2001.1.321

Information

Received: 14 December 2000; Revised: 21 May 2001; Accepted: 25 May 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0969.57014
MathSciNet: MR1835260
Digital Object Identifier: 10.2140/agt.2001.1.321

Subjects:
Primary: 57M25
Secondary: 57M27, 57M50

Rights: Copyright © 2001 Mathematical Sciences Publishers

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