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.

中文翻译：

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二重准交替链接，Khovanov 同源和瞬时子同源

我们引入了一类严格包含准交替链接的链接，其中 mod 2 减少的 Khovanov 同源性总是很薄。我们计算这种链接的双分支覆盖的框架瞬时子同源性。将链接上的某些虚线标记与分支覆盖上的束数据对齐，我们还提供了在存在非平凡实 3 平面束的情况下框架瞬时子同源性的许多计算。我们讨论了从具有 mod 2 系数的链接的扭曲 Khovanov 同源性到双分支覆盖的框架瞬时子同源性的光谱序列的证据。我们还讨论了相关的 mod 4 分级。