Rasmussen invariants of Whitehead doubles and other satellites

2022/08/29 by Lukas Lewark, Claudius Zibrowius, Lewark, Lukas +1 · 1 citation
Mathematics · #57K10 #57K18 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2208.13612

openalex publication_date 2022/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove formulae for the \mathbbF₂-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 τ.

Cited by

• 2-cabling and tangle operators in Khovanov theory

Related

• The Ozsváth-Szabó and Rasmussen concordance invariants are not equal
• A Rasmussen invariant for links in \mathbbRP³
• A Remark on the Lewark-Zibrowius Invariant
• Satellite Operations and θ
• A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds