Homologically thin, non-quasi-alternating links

We exhibit the first examples of links which are homologically thin but not quasi-alternating. To show that they are not quasi-alternating, we argue that none of their branched double-covers bounds a negative definite 4-manifold with non-torsion $H_1$. Using this method, we also complete the determination of the quasi-alternating pretzel links.

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Published 1 January 2010