 Heegaard Floer cobordism map

A smooth oriented cobordism $W:Y_1\to Y_2$ with a Spin-c structure induces $U$-equivariant maps $F_{W,\mathfrak{s}}^{\circ }$ 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 isThe 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.