Khovanov homology in characteristic two and involutive monopole Floer homology

2016/10/27 by Francesco Lin, Lin, Francesco
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1610.08866

openalex publication_date 2016/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the conjugation involution in Seiberg-Witten theory in the context of the Ozsváth-Szabó and Bloom's spectral sequence for the branched double cover of a link L in S³. We prove that there exists a spectral sequence of \mathbbF[Q]/Q²-modules (where Q has degree -1) which converges to \widetildeHMI_*(Σ(L)), an involutive version of the monopole Floer homology of the branched double cover, and whose E²-page is a version of Bar Natan's characteristic two Khovanov homology of the mirror of L. We conjecture that an analogous result holds in the setting of Pin(2)-monopole Floer homology.

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