We revisit Rozansky’s construction of Khovanov homology for links in , extending it to define the Khovanov homology for links L in for any r. The graded Euler characteristic of can be used to recover WRT invariants at certain roots of unity and also recovers the evaluation of L in the skein module of Hoste and Przytycki when L is null-homologous in . The construction also allows for a clear path toward defining a Lee’s homology and associated s-invariant for such L, which we will explore in an upcoming paper. We also give an equivalent construction for the Khovanov homology of the knotification of a link in and show directly that this is invariant under handle-slides, in the hope of lifting this version to give a stable homotopy type for such knotifications in a future paper.
Michigan Math. J.
70(4):
675-748
(October 2021).
DOI: 10.1307/mmj/1594281620
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