= Whitney disk class
{c}
{title2=$\pi_2(\mathbf x,\mathbf y)$}
For intersection generators $\mathbf x,\mathbf y$, a Whitney disk is a map of a disk into the <symmetric product>, with its two boundary semicircles mapped to the two product tori and its endpoints mapped to $\mathbf x,\mathbf y$. Its homotopy class belongs to $\pi_2(\mathbf x,\mathbf y)$. Projecting it to the <Heegaard surface> gives an integral domain. With the surface oriented, the convention is $\partial_\alpha D=\mathbf y-\mathbf x$. The obstruction to a disk is the class $\epsilon(\mathbf x,\mathbf y)\in H_1(Y)$ obtained by joining the points along alpha arcs and returning along beta arcs. In the Heegaard Floer setup, its vanishing is equivalent to equality of the generators' <Spin-c structures>; for the rational homology sphere diagrams this is equivalent to $\pi_2(\mathbf x,\mathbf y)\ne\varnothing$.
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