Sutured Floer homology, sutured TQFT and noncommutative QFT
نویسندگان
چکیده
منابع مشابه
The sutured Floer homology polytope
Using sutured Floer homology (in short SFH) I will define a polytope inside the second relative cohomology group of a sutured manifold. This is a generalization of the dual Thurston norm polytope of a link-complement studied by Ozsvath and Szabo using link Floer homology. The polytope is maximal dimensional under certain conditions. Moreover, surface decompositions correspond to the faces of th...
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We define a torsion invariant for balanced sutured manifolds and show that it agrees with the Euler characteristic of sutured Floer homology. The torsion is easily computed and shares many properties of the usual Alexander polynomial.
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We define the action of the homology group H1(M,∂M) on the sutured Floer homology SFH(M,γ). It turns out that the contact invariant EH(M,γ, ξ) is usually sent to zero by this action. This fact allows us to refine an earlier result proved by Ghiggini and the author. As a corollary, we classify knots in #(S × S) which have simple knot Floer homology groups: They are essentially the Borromean knots.
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In [28], Lawrence Roberts, extending the work of Ozsváth and Szabó in [23], showed how to associate to a link, L, in the complement of a fixed unknot, B ⊂ S, a spectral sequence whose E term is the Khovanov homology of a link in a thickened annulus defined in [2], and whose E term is the knot Floer homology of the preimage of B inside the double-branched cover of L. In [6], we extended [23] in ...
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I will talk about recent investigations of contact elements in the sutured Floer homology of solid tori, as part of the (1 + 1)-dimensional TQFT defined by Honda-Kazez-Matic. The Z2 sutured Floer homology vector spaces in this case form a ”categorification of Pascal’s triangle”, a triangle of vector spaces, with contact elements corresponding to chord diagrams and forming distinguished subsets ...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2011
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2011.11.2681