Link Floer Homology Categorifies the Conway Function
نویسندگان
چکیده
منابع مشابه
Singular link Floer homology
We define a grid presentation for singular links, i.e. links with a finite number of rigid transverse double points. Then we use it to generalize link Floer homology to singular links. Besides the consistency of its definition, we prove that this homology is acyclic under some conditions which naturally make its Euler characteristic vanish. Introduction Since the Jones polynomial was categorifi...
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Link Floer homology is an invariant for links defined using a suitable version of Lagrangian Floer homology. In an earlier paper, this invariant was given a combinatorial description with mod 2 coefficients. In the present paper, we give a self-contained presentation of the basic properties of link Floer homology, including an elementary proof of its invariance. We also fix signs for the differ...
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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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We prove that, for a link L in a rational homology 3–sphere, the link Floer homology detects the Thurston norm of its complement. This result has been proved by Ozsváth and Szabó for links in S . As an ingredient of the proof, we show that knot Floer homology detects the genus of null-homologous links in rational homology spheres, which is a generalization of an earlier result of the author. Ou...
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We define a new combinatorial complex computing the hat version of link Floer homology over Z/2Z, which turns out to be significantly smaller than the Manolescu–Ozsváth–Sarkar one.
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2016
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091515000528