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Holomorphic disks and knot invariants
- P. Ozsváth, Z. Szabó
- Mathematics
- 6 September 2002
Holomorphic disks and topological invariants for closed three-manifolds
- P. Ozsváth, Z. Szabó
- Mathematics
- 25 January 2001
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 , these…
Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary
- P. Ozsváth, Z. Szabó
- Mathematics
- 16 October 2001
Knot Floer homology and the four-ball genus
- P. Ozsváth, Z. Szabó
- Mathematics
- 14 January 2003
We use the knot filtration on the Heegaard Floer complex to define an integer invariant tau(K) for knots. Like the classical signature, this invariant gives a homomorphism from the knot concordance…
On the Heegaard Floer homology of branched double-covers
- P. Ozsváth, Z. Szabó
- Mathematics
- 9 September 2003
Holomorphic disks and three-manifold invariants: Properties and applications
- P. Ozsváth, Z. Szabó
- Mathematics
- 24 May 2001
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 ∈ Spin…
Holomorphic disks and genus bounds
- P. Ozsváth, Z. Szabó
- Mathematics
- 27 November 2003
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 the…
On knot Floer homology and lens space surgeries
- P. Ozsváth, Z. Szabó
- Mathematics
- 2 March 2003
Holomorphic triangles and invariants for smooth four-manifolds
- P. Ozsváth, Z. Szabó
- Mathematics
- 16 October 2001
On the Floer homology of plumbed three-manifolds
- P. Ozsváth, Z. Szabó
- Mathematics
- 26 March 2002
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, all…
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