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arXiv · 2208.13612

Rasmussen invariants of Whitehead doubles and other satellites

Lukas Lewark·Claudius Zibrowius
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Abstract

We prove formulae for the $\mathbb{F}_2$-Rasmussen invariant of satellite knots of patterns with wrapping number 2, using the multicurve technology for Khovanov and Bar-Natan homology developed by Kotelskiy, Watson, and the second author. A new concordance homomorphism, which is independent of the Rasmussen invariant, plays a central role in these formulae. We also explore whether similar formulae hold for the Ozsv\'ath-Szab\'o invariant $\tau$.

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BibTeXRIS

Lukas Lewark, Claudius Zibrowius. 2022-08-29. Rasmussen invariants of Whitehead doubles and other satellites. https://doi.org/10.1515/crelle-2024-0061

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