Volume 1, issue 1 (2001)

Download this article
For printing
Recent Issues

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
On McMullen's and other inequalities for the Thurston norm of link complements

Oliver T Dasbach and Brian S Mangum

Algebraic & Geometric Topology 1 (2001) 321–347

arXiv: math.GT/9911172

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
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27, 57M50
References
Forward citations
Publication
Received: 14 December 2000
Revised: 21 May 2001
Accepted: 25 May 2001
Published: 31 May 2001
Authors
Oliver T Dasbach
University of California
Riverside
Department of Mathematics
Riverside CA 92521-0135
USA
http://www.math.ucr.edu/~kasten
Brian S Mangum
Barnard College
Columbia University
Department of Mathematics
New York NY 10027
USA