Mathematische Annalen

, Volume 373, Issue 1–2, pp 489–516 | Cite as

Bar-Natan’s deformation of Khovanov homology and involutive monopole Floer homology

  • Francesco LinEmail author


We study the conjugation involution in Seiberg–Witten theory in the context of Ozsváth–Szabó and Bloom’s spectral sequence for the branched double cover of a link L in \(S^3.\) We prove that there exists a spectral sequence of \(\mathbb {F}[Q]/Q^2\)-modules (where Q has degree \(-1\)) which converges to \(\widetilde{ HMI }_*(\Sigma (L)),\) an involutive version of the monopole Floer homology of the branched double cover, and whose \(E^2\)-page is a version of Bar-Natan’s deformation of Khovanov homology in characteristic two of the mirror of L.



The author would like to thank Paolo Aceto, Ciprian Manolescu, Peter Ozsváth and Zoltán Szabó for the helpful discussions, and the anonymous referee for providing many constructive comments. This work was partially supported by the Shing-Shen Chern Membership Fund and the IAS Fund for Math.


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Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.School of Mathematics, Institute for Advanced StudyPrincetonUSA

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