Two-fold quasi-alternating links, Khovanov homology and instanton homology
arXiv:1605.05394 · doi:10.4171/QT/106
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.
arXiv comment29 pages, 14 figures
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Cited by in corpus (7)
- Framed instanton homology and concordance
- Instanton Floer homology, sutures, and Heegaard diagrams
- Instanton Floer homology of almost-rational plumbings
- Links all of whose cyclic branched covers are L-spaces
- Thin links and Conway spheres
- Framed instanton homology and concordance, II
- Traceless Character Varieties, the Link Surgeries Spectral Sequence, and Khovanov Homology