منابع مشابه
Heegaard Floer Homology as Morphism Spaces
In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The present formulation is closer in spirit to the usual TQFT framework, and allows a more direct comparison with Fukaya-categorical constructions. The result also leads to various dualities in bordered Floer homology.
متن کاملInvolutive Heegaard Floer Homology
Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to Z4-equivariant Seiberg-Witten Floer homology. Further, we obtain two new invariants of homology cobordism, d and d̄, and two invariants of smooth knot concordance, V 0 and V 0. We also develop a formula for the involutive Heeg...
متن کاملCovering spaces and Q-gradings on Heegaard Floer homology
Heegaard Floer homology, first introduced by P. Ozsváth and Z. Szabó in [OS04b], associates to a 3-manifold Y a family of relatively graded abelian groups HF (Y, t), indexed by Spin structures t on Y . In the case that Y is a rational homology sphere, Ozsváth and Szabó lift the relative Z-grading to an absolute Q-grading [OS06]. This induces a relative Q-grading on ⊕ t∈Spin(Y ) HF (Y, t). In th...
متن کاملHeegaard diagrams and Floer homology
We review the construction of Heegaard–Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link complement, the slice genus of a knot, and the unknotting number of a knot. We emphasize the application to the Thurston norm, and illustrate the theory in the ...
متن کاملHeegaard Floer Homology and Alternating Knots
In [23] we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y , which is closely related to the Heegaard Floer homology of Y (c.f. [21]). In this paper we investigate some properties of these knot homology groups for knots in the three-sphere. We give a combinatorial description for the generators of the chain complex and their gradings. With the help of th...
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ژورنال
عنوان ژورنال: Quantum Topology
سال: 2011
ISSN: 1663-487X
DOI: 10.4171/qt/25