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Holomorphic disks and knot invariants
Abstract We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the Heegaard Floer homologies for three-manifolds defined in an earlier paper. We set upExpand
Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary
Abstract In Ozsvath and Szabo (Holomorphic triangles and invariants for smooth four-manifolds, math. SG/0110169, 2001), we introduced absolute gradings on the three-manifold invariants developed inExpand
Holomorphic disks and topological invariants for closed three-manifolds
The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y, equipped with a Spiny structure. Given a Heegaard splitting of Y = U 0o U Σ U 1 , theseExpand
On knot Floer homology and lens space surgeries
Abstract In an earlier paper, we used the absolute grading on Heegaard Floer homology HF + to give restrictions on knots in S 3 which admit lens space surgeries. The aim of the present article is toExpand
On the Heegaard Floer homology of branched double-covers
Abstract Let L ⊂ S 3 be a link. We study the Heegaard Floer homology of the branched double-cover Σ ( L ) of S 3 , branched along L. When L is an alternating link, HF ^ of its branched double-coverExpand
Holomorphic disks and genus bounds
We prove that, like the Seiberg-Witten monopole homology, the Heegaard Floer homology for a three-manifold determines its Thurston norm. As a consequence, we show that knot Floer homology detects theExpand
Holomorphic disks and three-manifold invariants: Properties and applications
In [27], we introduced Floer homology theories HF - (Y,s), HF∞(Y,s), HF + (Y, t), HF(Y,s),and HF red (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spiny structures s ∈ SpinExpand
Holomorphic triangles and invariants for smooth four-manifolds
Abstract In earlier articles, the authors introduced invariants for closed, oriented three-manifolds, defined using a variant of Lagrangian Floer homology in the symmetric products of RiemannExpand
On the Floer homology of plumbed three-manifolds
We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, allExpand
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