Quantum Topology


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Volume 9, Issue 1, 2018, pp. 167–205
DOI: 10.4171/QT/106

Published online: 2018-02-01

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

Christopher Scaduto[1] and Matthew Stoffregen[2]

(1) State University of New York, Stony Brook, USA
(2) University of California, Los Angeles, USA

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.

Keywords: Quasi-alternating, instanton homology, Khovanov homology, knots

Scaduto Christopher, Stoffregen Matthew: Two-fold quasi-alternating links, Khovanov homology and instanton homology. Quantum Topol. 9 (2018), 167-205. doi: 10.4171/QT/106