Journal of Symplectic Geometry
Volume 15 (2017)
An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields
Pages: 51 – 90
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 the relative one and that it is compatible with the maps induced by cobordisms. We also prove that if $\xi$ is a contact structure on $Y$, then the grading of the contact invariant $c(\xi)$ is the homotopy class of $\xi$.