Absolute grading in Heegaard Floer homology

ID: absolute-grading-in-heegaard-floer-homology

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 having degree zero. Multiplication by has degree , and a Heegaard Floer cobordism map has degree . The correction term is the lowest grading of the image of in for a rational homology sphere. A pure tower then has bottom plus degree and top minus degree in the minus convention. Keeping that shift explicit prevents errors of two in surgery and mixed-invariant calculations.

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