# 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.

## 6 Citations

### Higher-dimensional Heegaard Floer homology and Hecke algebras

- Mathematics
- 2022

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

- Mathematics
- 2022

. 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

- Mathematics
- 2021

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

- Mathematics
- 2022

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

- Mathematics
- 2021

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

- Mathematics
- 2020

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…

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