Link Floer homology and the Thurston norm
Peter Ozsvath, Zoltan Szabo
TL;DR
This paper demonstrates that link Floer homology can determine the Thurston norm of a link complement and explores its applications to alternating links and specific examples.
Contribution
It establishes a connection between link Floer homology and the Thurston norm, providing new tools for studying link complements.
Findings
Link Floer homology detects the Thurston norm.
Thurston polytope of an alternating link is dual to the Newton polytope of its Alexander polynomial.
Computed Thurston polytopes for several specific links.
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · semigroups and automata theory