Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 1, Number 1 (2001), 321-347.
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 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.
Algebr. Geom. Topol., Volume 1, Number 1 (2001), 321-347.
Received: 14 December 2000
Revised: 21 May 2001
Accepted: 25 May 2001
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Dasbach, Oliver T; Mangum, Brian S. On McMullen's and other inequalities for the Thurston norm of link complements. Algebr. Geom. Topol. 1 (2001), no. 1, 321--347. doi:10.2140/agt.2001.1.321. https://projecteuclid.org/euclid.agt/1513882596