Heegaard Floer correction terms and rational genus bounds

@article{Ni2012HeegaardFC,
  title={Heegaard Floer correction terms and rational genus bounds},
  author={Yi Ni and Zhongtao Wu},
  journal={Advances in Mathematics},
  year={2012},
  volume={267},
  pages={360-380}
}
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29 Citations
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29 Citations

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References

SHOWING 1-10 OF 34 REFERENCES
Knot Floer homology and rational surgeries
Let K be a rationally null-homologous knot in a three-manifold Y . We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold…
Link Floer homology detects the Thurston norm
We prove that, for a link L in a rational homology 3–sphere, the link Floer homology detects the Thurston norm of its complement. This result has been proved by Ozsvath and Szabo for links in S^3. As…
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 the…
Floer homology and knot complements
We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call CF_r. It…
Knot Floer homology and the four-ball genus
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…
Knots with small rational genus
If K is a rationally null-homologous knot in a 3-manifold M, the rational genus of K is the infimum of -\chi(S)/2p over all embedded orientable surfaces S in the complement of K whose boundary wraps…
On Floer homology and the Berge conjecture on knots admitting lens space surgeries
We complete the first step in a two-part program proposed by Baker, Grigsby, and the author to prove that Berge’s construction of knots in the three-sphere which admit lens space surgeries is…
Covering spaces and Q-gradings on Heegaard Floer homology
Heegaard Floer homology, first introduced by P. Ozsvath and Z. Szabo 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…
Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
Similar to knots in S 3 , any knot in a lens space has a grid diagram from which one can combinatorially compute all of its knot Floer homology invariants. We give an explicit description of the…
Holomorphic disks and knot invariants
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