Journal of Symplectic Geometry

Volume 15 (2017)

Number 1

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

Pages: 51 – 90



Yang Huang (Centre for Quantum Geometry of Moduli Spaces, Aarhus University, Aarhus, Denmark)

Vinicius G. B. Ramos (Instituto Nacional de Matemtica Pura e Aplicada, Rio de Janeiro, Brazil)


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 $\xi$.

Published 28 April 2017