Absolute gradings on ECH and Heegaard Floer homology

Abstract

In joint work with Yang Huang, we defined a canonical absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields. A similar grading was defined on embedded contact homology by Michael Hutchings. In this paper we show that the isomorphism between these homology theories defined by Colin, Ghiggini, and Honda preserves this grading.