Link cobordisms and functoriality in link Floer homology
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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My research at UCSD has focused on advancing our understanding of Khovanov’s homology theory for links and link cobordisms, first introduced in [10]. His theory is a “categorification” of the Jones polynomial V (L), so described because it associates to any link L a complex Kh(L) of bigraded modules whose graded Euler characteristic is V (L). Not only is the homotopy type of Kh(L) a link invari...
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Abstract. This paper is devoted to the study of algebraic structures leading to link homology theories. The originally used structures of Frobenius algebra and/or TQFT are modified in two directions. First, we refine 2–dimensional cobordisms by taking into account their embedding into R. Secondly, we extend the underlying cobordism category to a 2–category, where the usual relations hold up to ...
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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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ژورنال
عنوان ژورنال: Journal of Topology
سال: 2018
ISSN: 1753-8416,1753-8424
DOI: 10.1112/topo.12085