Signatures, Heegaard Floer correction terms and quasi-alternating links

2013/02/13 by Paolo Lisca, Lisca, Paolo, Brendan Owens +1 · 1 citation
Mathematics · #57M25 #57M27 (Primary) 57Q60 (Secondary) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #msc:57M27 #msc:57Q60

paper · pdf · doi:10.48550/arxiv.1302.3190

V2: Improved exposition incorporating referee's suggestions; 3 figures, 6 pages. Accepted for publication by the Proceedings of the American Mathematical Society

openalex publication_date 2013/02/13 · arxiv created 2013/05/22 · arxiv updated 2013/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Turaev showed that there is a well-defined map assigning to an oriented link L in the three-sphere a Spin structure t₀ on Sigma(L), the 2-fold cover of S³ 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), t₀).

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• Extending Quasi-alternating Links II

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