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On combinatorial link Floer homology
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 2Expand
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Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Froyshov's correction term in this setting is anExpand
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On the Khovanov and knot Floer homologies of quasi-alternating links
Quasi-alternating links are a natural generalization of alternating links. In this paper, we show that quasi-alternating links are "homologically thin" for both Khovanov homology and knot FloerExpand
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Heegaard Floer homology and integer surgeries on links
Let L be a link in an integral homology three-sphere. We give a description of the Heegaard Floer homology of integral surgeries on L in terms of some data associated to L, which we call a completeExpand
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Seiberg{Witten{Floer stable homotopy type of three-manifolds with b1 =0
Using Furuta’s idea of nite dimensional approximation in Seiberg{Witten theory, we rene Seiberg{Witten Floer homology to obtain an invariant of homology 3{spheres which lives in the S 1 {equivariantExpand
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A combinatorial description of knot Floer homology
Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains areExpand
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Involutive 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 $\mathbb{Z}_4$-equivariantExpand
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A concordance invariant from the Floer homology of double branched covers
Ozsvath and Szabo defined an analog of the Froyshov invariant in the form of a correction term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-sphere branchedExpand
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Nilpotent slices, Hilbert schemes, and the Jones polynomial
Seidel and Smith have constructed an invariant of links as the Floer cohomology for two Lagrangians inside a complex affine variety Y. This variety is the intersection of a semisimple orbit with aExpand
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A two-variable series for knot complements
The physical 3d $\mathcal{N}=2$ theory T[Y] was previously used to predict the existence of some 3-manifold invariants $\hat{Z}_{a}(q)$ that take the form of power series with integer coefficients,Expand
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