The categorification of the Kauffman bracket skein module of \(R\)\(P^3\)
Keywords:Khovanov homology, categorification, skein module, Kauman bracket
AbstractKhovanov homology, an invariant of links in R3, is a graded homology theory that categorifies the Jones polynomial in the sense that the graded Euler characteristic of the homology is the Jones polynomial. Asaeda, Przytycki and Sikora generalized this construction by defining a double graded homology theory that categorifies the Kauman bracket skein module of links in I-bundles over surfaces, except for the surface RP2, where the construction fails due to strange behaviour of links when projected to the non-orientable surface RP2. This paper categorifies the missing case of the twisted I-bundle over RP2, RP2eI RP3 n fg, by redefining the dierential in the Khovanov chain complex in a suitable manner. 10.1017/S0004972713000105
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