Link Floer homology and the Thurston norm

2006/01/25 by Peter Ozsváth, Zoltán Szabó, Ozsvath, Peter +1 · 2 citations
Computer Science · Mathematics · #53D #57R #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0601618

openalex publication_date 2006/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants

Cited by

• Quantum Invariants and Fiberedness
• Skein exact triangles in knot Floer homology

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