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

Francesco Lin

doi:10.1007/s00208-018-1675-y

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

Francesco Lin

Mathematics

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Abstract

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 F[Q] / Q ² -modules (where Q has degree - 1) which converges to HMI~ _∗ (Σ (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.

Original language	English (US)
Pages (from-to)	489-516
Number of pages	28
Journal	Mathematische Annalen
Volume	373
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-018-1675-y
State	Published - Feb 8 2019

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General Mathematics

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title = "Bar-Natan{\textquoteright}s deformation of Khovanov homology and involutive monopole Floer homology",

abstract = " We study the conjugation involution in Seiberg–Witten theory in the context of Ozsv{\'a}th–Szab{\'o} and Bloom{\textquoteright}s spectral sequence for the branched double cover of a link L in S 3 . We prove that there exists a spectral sequence of F[Q] / Q 2 -modules (where Q has degree - 1) which converges to HMI~ ∗ (Σ (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{\textquoteright}s deformation of Khovanov homology in characteristic two of the mirror of L.",

author = "Francesco Lin",

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PY - 2019/2/8

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N2 - 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 F[Q] / Q 2 -modules (where Q has degree - 1) which converges to HMI~ ∗ (Σ (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.

AB - 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 F[Q] / Q 2 -modules (where Q has degree - 1) which converges to HMI~ ∗ (Σ (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.

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

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