Signatures, Heegaard Floer correction terms and quasi-alternating links

TL;DR

This paper establishes a precise relationship between the signature of quasi-alternating links and the Heegaard Floer correction terms of their branched double covers, extending previous results in the field.

Contribution

It proves that for quasi-alternating links, the link signature equals minus four times the Heegaard Floer correction term of the associated branched cover, generalizing earlier findings.

Findings

Signature equals minus four times the correction term for quasi-alternating links

Generalization of Manolescu-Owens and Donald-Owens results

Provides a new link between link invariants and 3-manifold invariants

Abstract

Turaev showed that there is a well-defined map assigning to an oriented link L in the three-sphere a Spin structure t_0 on Sigma(L), the 2-fold cover of S^3 branched along L. We prove, generalizing results of Manolescu-Owens and Donald-Owens, that for an oriented quasi-alternating link L the signature of L equals minus four times the Heegaard Floer correction term of (Sigma(L), t_0).