On the slice-ribbon conjecture for pretzel knots

Lecuona, Ana G¹

¹Institut de Mathématiques de Marseille, Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

Algebraic and Geometric Topology, Tome 15 (2015) no. 4, pp. 2133-2173

Résumé

We give a necessary, and in some cases sufficient, condition for sliceness inside the family of pretzel knots P(p1,…,pn) with one pi even. The 3–stranded case yields two interesting families of examples: The first consists of knots for which the nonsliceness 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.

Détail

DOI : 10.2140/agt.2015.15.2133

Classification : 57M25
Keywords: Slice-ribbon conjecture, pretzel knots, rational homology balls

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