On the slice-ribbon conjecture for pretzel knots

Lecuona, Ana G

doi:10.2140/agt.2015.15.2133

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On the slice-ribbon conjecture for pretzel knots

Ana G Lecuona

Algebraic & Geometric Topology 15 (2015) 2133–2173

DOI: 10.2140/agt.2015.15.2133

Abstract

We give a necessary, and in some cases sufficient, condition for sliceness inside the family of pretzel knots $P (p_{1}, \dots, p_{n})$ with one $p_{i}$ 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.

Keywords

Slice-ribbon conjecture, pretzel knots, rational homology balls

Mathematical Subject Classification 2010

Primary: 57M25

References

Publication

Received: 23 April 2014

Revised: 27 October 2014

Accepted: 31 October 2014

Published: 10 September 2015

Authors

Ana G Lecuona
Institut de Mathématiques de Marseille Aix-Marseille Université CNRS, Centrale Marseille, I2M, UMR 7373 13453 Marseille France

Volume 15, issue 4 (2015)