Generalized Heegaard Floer correction terms

We make use of the action of $H_1(Y)$ in Heegaard Floer homology to generalize the Ozsv'ath-Szab'o correction terms for $3$-manifolds with standard ${\mathrm{HF}}^{\mathrm{\infty }}$. We establish the basic properties of these invariants: conjugation invariance, behavior under orientation reversal, additivity, and spin${}^c$ rational homology cobordism invariance.