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We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin structures, generalising the correction terms (or -invariants) defined by Ozsváth and Szabó for rational homology 3-spheres and, more generally, for 3-manifolds with standard HF. 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.
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Stefan Behrens, Marco Golla, Heegaard Floer correction terms, with a twist. Quantum Topol. 9 (2018), no. 1, pp. 1–37DOI 10.4171/QT/102