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, Two-fold quasi-alternating links, Khovanov homology and instanton homology. Quantum Topol. 9 (2018), no. 1, pp. 167–205DOI 10.4171/QT/106