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

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

2011-06-28

arxiv.org/abs/1106.5559v1

Mathematics

Geometric Topology

11 pages, 3 figures

Scientific paper

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.

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