Explicit formula for the Rasmussen invariant of odd pretzel knots

Yury Belousov; Vadim Stepaniuk

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arXiv · 2610.24083

Explicit formula for the Rasmussen invariant of odd pretzel knots

Yury Belousov·Vadim Stepaniuk

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Abstract

We compute the Rasmussen s-invariant for all odd pretzel knots, giving an explicit closed formula. The formula extends to all slice-torus invariants that are invariant under mutation. In the absence of mutation invariance, we prove the formula under a mild condition on the pretzel parameters, which we conjecture to be unnecessary.

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BibTeX RIS

Yury Belousov, Vadim Stepaniuk. 2026-10-16. Explicit formula for the Rasmussen invariant of odd pretzel knots. https://arxiv.org/abs/2610.24083

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