Twisted skein homology (Q2878663)

In 2000, Khovanov defined a link homology theory by categorifying the Jones polynomial of links. It is called Khovanov homology, now.NEWLINENEWLINEIn 2004, \textit{M. M. Asaeda} et al. [Algebr. Geom. Topol. 4, 1177--1210 (2004; Zbl 1070.57008)] constructed a categorification of the Kauffman bracket skein module of I-bundles over surfaces by generalizing Khovanov's categorification. In [\textit{M. M. Asaeda} et al., Contemp. Math. 416, 1--8 (2006; Zbl 1138.57013)], they also constructed a categorification of the skein module of tangles.NEWLINENEWLINE\textit{L. Roberts} [Totally Twisted Khovanov Homology, \url{arXiv: 1109.0508}] introduced a version of characteristic-2 Khovanov homology called totally twisted Khovanov homology. The homology has a single \(\delta\)-grading. Roberts also gave a spanning tree model for the totally twisted Khovanov homology. \textit{T. C. Jaeger} [J. Knot Theory Ramifications 22, No. 6, Article ID 1350022 (2013; Zbl 1271.57018)] proved that for knots, the totally twisted Khovanov homology coincides with the \(\delta\)-graded reduced Khovanov homology. Here \(\delta\) is given by \(\delta = 2i-j\) where \(i\) and \(j\) are the homological grading and the quantum grading, respectively.NEWLINENEWLINEIn the paper under review, the authors apply the technique of totally twisted Khovanov homology to Asaeda, Przytycki and Sikora's categorification.