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 integer homology 3-spheres and, more generally, for 3-manifolds with standard ${\mathrm{HF}}^{\infty }$. 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.

24 pages, 2 figures; New proof of additivity (Proposition 3.7) based on a connected sum formula for twisted coefficients (Proposition 2.3); exposition improved, mainly in Section 4; Proposition 3.8 downgraded to an inequality due to an error in the previous version found by Adam Levine