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Bordered Heegaard Floer homology is an invariant for 3-manifolds, whichassociates to a surface F an algebra A(F), and to a 3-manifold Y with boundary,together with an orientation-preserving diffeomorphism from F to the boundaryof Y, a module over A(F). In a previous paper, we defined relative Z/2differential gradings on the algebra A(F) and the modules over it. In thispaper, we turn the relative grading into an absolute one, and show that theresulting Z/2-graded module is an invariant of the bordered 3-manifold.

An absolute Z/2 grading on bordered Heegaard Floer homology