Turaev torsion, definite 4-manifolds, and quasi-alternating knots

Abstract

We construct an infinite family of hyperbolic, homologically thin knots that are not quasi-alternating. To establish the latter, we argue that the branched double-cover of each knot in the family does not bound a negative definite 4-manifold with trivial first homology and bounded second betti number. This fact depends in turn on information from the correction terms in Heegaard Floer homology, which we establish by way of a relationship to, and calculation of, the Turaev torsion.

11 pages, 3 figures

References in corpus (3)

• Floer homology and knot complements
• On the Khovanov and knot Floer homologies of quasi-alternating links
• Surgery formula for the renormalized Euler characteristic of Heegaard Floer homology

Cited by in corpus (7)

• The reduced knot Floer complex
• A new obstruction of quasi-alternating links
• Genus two mutant knots with the same dimension in knot Floer and Khovanov homologies
• Strong Heegaard diagrams and strong L-spaces
• The Alexander module, Seifert forms, and categorification
• Thin links and Conway spheres
• A New property of quasi-alternating links