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Explicit formula for the Rasmussen invariant of odd pretzel knots
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
@misc{belousov2026explicit,
title = {{Explicit formula for the Rasmussen invariant of odd pretzel knots}},
author = {Yury Belousov and Vadim Stepaniuk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24083},
eprint = {2610.24083},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24083},
}
RIS
TY - UNPB
TI - Explicit formula for the Rasmussen invariant of odd pretzel knots
AU - Yury Belousov
AU - Vadim Stepaniuk
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24083
UR - https://arxiv.org/abs/2610.24083
AB - 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.
ER -