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arXiv · 2609.34522

Exceptional pretzel knots are not algebraically slice

Suman Saurabh
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Abstract

We prove that the Alexander polynomial of every knot in Lecuona's exceptional family of pretzel knots fails the Fox--Milnor condition. Consequently, none of these knots is algebraically or topologically slice. Together with work of Lecuona, Miller, and Kim--Lee--Song, this completes the slice--ribbon and topological-sliceness classifications for three-strand pretzel knots. It also removes the nonexceptional hypothesis from the Lecuona--Wand classification of prime fibered ribbon pretzel knots up to reordering of parameters.

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Suman Saurabh. 2026-09-28. Exceptional pretzel knots are not algebraically slice. https://arxiv.org/abs/2609.34522

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