= Absolute grading in Heegaard Floer homology
{title2=$\operatorname{gr}\in\mathbb Q$}
= Absolute Heegaard Floer grading
{synonym}
For a torsion <Spin-c structure>, the relative grading of <Heegaard Floer homology> lifts canonically to a rational absolute grading, normalized by the bottom plus generator of $S^3$ having degree zero. Multiplication by $U$ has degree $-2$, and a <Heegaard Floer cobordism map> has degree $(c_1^2-2\chi-3\sigma)/4$. The correction term $d(Y,\mathfrak s)$ is the lowest grading of the image of $HF^\infty$ in $HF^+$ for a rational homology sphere. A pure tower then has bottom plus degree $d$ and top minus degree $d-2$ in the $i<0$ minus convention. Keeping that shift explicit prevents errors of two in surgery and mixed-invariant calculations.
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