Heegaard Floer correction terms, with a twist

Abstract

We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin${}^c$ structures, generalising the correction terms (or $d$-invariants) defined by Ozsváth and Szabó for rational homology 3-spheres and, more generally, for 3-manifolds with standard HF${}^{\infty }$. Our twisted correction terms share many properties with their untwisted analogues. In particular, they provide restrictions on the topology of 4-manifolds bounding a given 3-manifold.