#### Volume 15, issue 4 (2015)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
On the slice-ribbon conjecture for pretzel knots

### Ana G Lecuona

Algebraic & Geometric Topology 15 (2015) 2133–2173
##### Abstract

We give a necessary, and in some cases sufficient, condition for sliceness inside the family of pretzel knots $P\left({p}_{1},\dots ,{p}_{n}\right)$ 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
Primary: 57M25