Link Floer homology and the Thurston norm

Abstract

We show that link Floer homology detects the Thurston norm of a link complement. As an application, we show that the Thurston polytope of an alternating link is dual to the Newton polytope of its multi-variable Alexander polynomial. To illustrate these techniques, we also compute the Thurston polytopes of several specific link complements.

Revised Section 3: improved exposition and corrected statement of Lemma 3.6. Also other minor revisions throughout

References in corpus (6)

• Floer homology and knot complements
• On the Floer homology of plumbed three-manifolds
• Heegaard Floer homology and alternating knots
• The support of the Khovanov's invariants for alternating knots
• Adiabatic limits of Seiberg-Witten equations on Seifert manifolds
• On the Heegaard Floer homology of a surface times a circle

Cited by in corpus (3)

• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Link Floer homology detects the Thurston norm
• The Thurston polytope for four-stranded pretzel links