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Bar Natan's deformation of Khovanov homology and involutive monopole Floer homology

Presented by: 
Francesco Lin Princeton University
Thursday 20th April 2017 - 15:15 to 16:15
INI Seminar Room 2
We study the conjugation involution in Seiberg-Witten theory in the context of the Ozsvath-Szabo and Bloom's spectral sequence for the branched double cover of a link L in S^3. We show that there exists a spectral sequence of F[Q]/Q^2-modules (where Q has degree −1) which converges to 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. We conjecture that an analogous result holds in the setting of Pin(2)-monopole Floer homology.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons