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Reveals explicit formulae for the Alexander polynomial of pretzel knots, suggesting new knot families with unique properties.
We provide explicit formulae for the Alexander polynomial of pretzel knots and establish several immediate corollaries, including the characterisation of pretzel knots with a trivial Alexander polynomial. As an application, we construct a new family of knots that are topologically slice, but not smoothly slice.
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Yury Belousov (2026) studied this question.
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