On the slice-ribbon conjecture for pretzel knots

Ana G. Lecuona

doi:10.2140/agt.2015.15.2133

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arXiv · 1309.0550

On the slice-ribbon conjecture for pretzel knots

Ana G. Lecuona

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Abstract

We give a necessary, and in some cases sufficient, condition for sliceness inside the family of pretzel knots $P (p_1,...,p_n)$ with one $p_i$ even. The three stranded case yields two interesting families of examples: the first consists of knots for which the non-sliceness is detected by the Alexander polynomial while several modern obstructions to sliceness vanish. The second family has the property that the correction terms from Heegaard-Floer homology of the double branched covers of these knots do not obstruct the existence of a rational homology ball; however, the Casson-Gordon invariants show that the double branched covers do not bound rational homology balls.

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Ana G. Lecuona. 2013-09-02. On the slice-ribbon conjecture for pretzel knots. https://doi.org/10.2140/agt.2015.15.2133

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