On the slice-ribbon conjecture for pretzel knots

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.

30 pages, 10 figures

References in corpus (2)

• Lens spaces, rational balls and the ribbon conjecture
• Sums of lens spaces bounding rational balls

Cited by in corpus (3)

• The topological sliceness of 3-strand pretzel knots
• A survey of the homology cobordism group
• Explicit Formulas for the Alexander Polynomial of Pretzel Knots