Algebraic & Geometric Topology

On the slice-ribbon conjecture for pretzel knots

Ana G Lecuona

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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.

Article information

Algebr. Geom. Topol., Volume 15, Number 4 (2015), 2133-2173.

Received: 23 April 2014
Revised: 27 October 2014
Accepted: 31 October 2014
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Slice-ribbon conjecture pretzel knots rational homology balls


Lecuona, Ana G. On the slice-ribbon conjecture for pretzel knots. Algebr. Geom. Topol. 15 (2015), no. 4, 2133--2173. doi:10.2140/agt.2015.15.2133.

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