 Relative grading in Heegaard Floer homology

For generators in the same Spin-c structure and a Whitney disk class $\psi$ joining them,The ambiguity is the divisibility of $c_1(\mathfrak{s})$ on $H_2(Y)$; a torsion determinant class gives an integer relative grading. Adding a sphere class changes $\mu$ by two and $n_z$ by one, so it leaves the difference unchanged. For a domain $D$, the index can be calculated as $\mu (D)=e(D)+n_{\mathbf{x}}(D)+n_{\mathbf{y}}(D)$, where $e$ is Euler measure and each $n_{\mathbf{x}}$ is the sum of averages of the four adjacent region multiplicities at the selected intersections.