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On
McMullen's and other inequalities for the Thurston norm of
link complements
Oliver T Dasbach and Brian S Mangum |
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Algebraic & Geometric Topology 1 (2001) 321–347
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arXiv: math.GT/9911172 |
Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27, 57M50
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References |
Forward citations |
Publication
Received: 14 December 2000
Revised: 21 May 2001
Accepted: 25 May 2001
Published: 31 May 2001
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Authors |
| Oliver T Dasbach | |
| University of California Riverside Department of Mathematics Riverside CA 92521-0135 USA |
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| http://www.math.ucr.edu/~kasten | |
| Brian S Mangum | |
| Barnard College Columbia University Department of Mathematics New York NY 10027 USA |
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