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-Honda preserves this grading.

中文翻译：

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ECH 和 Heegaard Floer 同源性的绝对分级

在与 Yang Huang 的合作中，我们通过定向 2 平面场的同伦类定义了 Heegaard Floer 同源性的规范绝对分级。Michael Hutchings 对嵌入式接触同源性定义了类似的分级。在本文中，我们表明 Colin-Ghiggini-Honda 定义的这些同源理论之间的同构保留了这种分级。