Two-fold quasi-alternating links, Khovanov homology and instanton homology

Christopher Scaduto; Matthew Stoffregen

doi:10.4171/qt/106

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arXiv · 1605.05394

Two-fold quasi-alternating links, Khovanov homology and instanton homology

Christopher Scaduto·Matthew Stoffregen

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Abstract

We introduce a class of links strictly containing quasi-alternating links for which mod 2 reduced Khovanov homology is always thin. We compute the framed instanton homology for double branched covers of such links. Aligning certain dotted markings on a link with bundle data over the branched cover, we also provide many computations of framed instanton homology in the presence of a non-trivial real 3-plane bundle. We discuss evidence for a spectral sequence from the twisted Khovanov homology of a link with mod 2 coefficients to the framed instanton homology of the double branched cover. We also discuss the relevant mod 4 gradings.

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Christopher Scaduto, Matthew Stoffregen. 2016-05-17. Two-fold quasi-alternating links, Khovanov homology and instanton homology. https://doi.org/10.4171/qt%2F106

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