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

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  • Yang Huang
  • ,
  • Vinicius G.B. Ramos, Instituto Nacional de Matemtica Pura e Aplicada

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.

Original languageEnglish
JournalJournal of Symplectic Geometry
Pages (from-to)51-90
Number of pages40
Publication statusPublished - 1 Jan 2017

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