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

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 ξ is a contact structure on Y, then the grading of the contact invariant c(ξ) is the homotopy class of ξ.

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