= Heegaard Floer cobordism map
{c}
{title2=$F^\circ_{W,\mathfrak s}$}
A smooth oriented <cobordism> $W:Y_1\to Y_2$ with a <Spin-c structure> induces $U$-equivariant maps $F^\circ_{W,\mathfrak s}$ on the corresponding <Heegaard Floer homology> groups. A <handle decomposition> defines the maps using generator selection for one- and three-handles and holomorphic triangle counts for two-handles. Composition sums over extensions of the prescribed Spin-c structures. When the boundary determinant classes are torsion, the absolute grading shift is
$$
\Delta(W,\mathfrak s)=\frac{c_1(\mathfrak s)^2-2\chi(W)-3\sigma(W)}4.
$$
The square is defined using the rational relative lift. If $b_2^+(W)>0$, the infinity map vanishes. Between rational homology spheres, when $b_1(W)=b_2^+(W)=0$, the infinity map is an isomorphism of Laurent towers.
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