Rasmussen invariants of Whitehead doubles and other satellites

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 Ozsváth-Szabó invariant $\tau$.

49 pages, 16 figures, 7 tables. Published version

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