• Corpus ID: 219558227

Applications of higher-dimensional Heegaard Floer homology to contact topology

@article{Colin2020ApplicationsOH,
  title={Applications of higher-dimensional Heegaard Floer homology to contact topology},
  author={Vincent Colin and Ko Honda and Yin Tian},
  journal={arXiv: Symplectic Geometry},
  year={2020}
}
The goal of this paper is to set up the general framework of higher-dimensional Heegaard Floer homology, define the contact class, and use it to give an obstruction to the Liouville fillability of a contact manifold and a sufficient condition for the Weinstein conjecture to hold. We discuss several classes of examples including those coming from analyzing a close cousin of symplectic Khovanov homology and the analog of the Plamenevskaya invariant of transverse links. 
View PDF on arXiv
6 Citations
Highly Influential Citations
1
Background Citations
3
Methods Citations
1
Results Citations
1

6 Citations

Higher-dimensional Heegaard Floer homology and Hecke algebras

Given a closed oriented surface Σ of genus greater than 0, we construct a map F from the higher-dimensional Heegaard Floer homology of the cotangent fibers of T ∗Σ to the Hecke algebra associated to…

An example of higher-dimensional Heegaard Floer homology

. We count pseudoholomorphic curves in the higher-dimensional Heegaard Floer homology of disjoint cotangent fibers of a two dimensional disk. We show that the resulting algebra is isomorphic to the…

Closed-open morphisms on periodic Floer homology

In this note, we investigate homomorphisms from the periodic Floer homology (PFH) to the quantitative Heegaard Floer homology. We call the homomorphisms closed-open morphisms. Under certain…

On PFH and HF spectral invariants

In this note, we define the link spectral invariants by using the cylindrical formulation of the quantitative Heegaard Floer homology. We call them HF spectral invariants. We deduce a relation…

Simplified SFT moduli spaces for Legendrian links

A BSTRACT . We study moduli spaces M of holomorphic maps U to R 4 with boundaries on the Lagrangian cylinder over a Legendrian link Λ ⊂ ( R 3 , ξ std ) . We allow our domains, ˙Σ , to have…

Generalizations of planar contact manifolds to higher dimensions

Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated planar contact…

References

SHOWING 1-10 OF 57 REFERENCES

On the contact class in Heegaard Floer homology

We present an alternate description of the Ozsvath-Szabo contact class in Heegaard Floer homology. Using our contact class, we prove that if a contact structure (M,\xi) has an adapted open book…

ON THE CONSTRUCTION OF CONTACT SUBMANIFOLDS WITH PRESCRIBED TOPOLOGY

We prove the existence of contact submanifolds realizing the Poincare dual of the top Chern class of a complex vector bundle over a closed contact manifold. This result is analogue in the contact…

Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions

The proof of the equivalence between the hat versions of Heegaard Floer homology and embedded contact homology is sketched and expressed in terms of an open book decomposition of the ambient manifold.

Transverse knots and Khovanov homology

We define an invariant of transverse links in the standard contact 3-sphere as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking…

The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II

This paper is the sequel to "The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I" and is devoted to proving some of the technical parts of the…

A long exact sequence for symplectic Floer cohomology

Khovanov homology, open books, and tight contact structures

Legendrian contact homology in $P \times \mathbb{R}$

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P x R, where P is an exact symplectic manifold, is established. The class of such contact…

Khovanov homology from Floer cohomology

This paper realises the Khovanov homology of a link in S 3 S^3 as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is…

A cylindrical reformulation of Heegaard Floer homology

We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold U a0;1c R, where U is the Heegaard surface, instead of Sym g .U/. We then show that the entire…
...