# A topological grading on bordered Heegaard Floer homology

@article{Huang2012ATG, title={A topological grading on bordered Heegaard Floer homology}, author={Yang Huang and Vinicius G. B. Ramos}, journal={arXiv: Geometric Topology}, year={2012} }

In this paper, we construct a canonical grading on bordered Heegaard Floer homology by homotopy classes of nonvanishing vector fields. This grading is a generalization of our construction of an absolute grading on Heegaard Floer homology and it extends the well-known grading with values in a noncommutative group defined by Lipshitz-Ozsv\'ath-Thurston.

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## References

SHOWING 1-7 OF 7 REFERENCES

An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields

- Mathematics
- 2011

For a closed oriented 3-manifold Y, we define an absolute grading on the Heegaard Floer homology groups of Y by homotopy classes of oriented 2-plane fields. We show that this absolute grading refines…

Heegaard Floer homology as morphism spaces

- Mathematics
- 2011

In this paper we prove another pairing theorem for bordered Floer homology. Unlike the original pairing theorem, this one is stated in terms of homomorphisms, not tensor products. The present…

A cylindrical reformulation of Heegaard Floer homology

- Mathematics
- 2006

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…

Classes d'homotopie de champs de vecteurs Morse-Smale sans singularit\'e sur les fibr\'es de Seifert

- Mathematics
- 2003

In the first part of this paper, we consider smooth maps from a compact orientable 3-manifold without boundary to the 2-sphere. We give a geometric criterion to decide whether two given maps are…

Bordered Floer homology for sutured manifolds

- Mathematics
- 2009

We define a sutured cobordism category of surfaces with boundary and 3-manifolds with corners. In this category a sutured 3-manifold is regarded as a morphism from the empty surface to itself. In the…

Holomorphic disks and three-manifold invariants: Properties and applications

- Mathematics
- 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…

Emmanuel Dufraine Classes d ’ homotopie de champs de vecteurs Morse - Smale sans singularité sur les fibrés de Seifert

- 2011