An enhanced Khovanov TQFT with basepoint actions is invariant under connected sum with RP²(-2), vanishes for RP²(+2), answers a Lipshitz-Sarkar question, and yields functoriality for pointed Khovanov homology.
Scott Carter and Masahico Saito, Knotted surfaces and their diagrams, Mathematical Surveys and Monographs, vol
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Basepoints in Khovanov homology and nonorientable surfaces
An enhanced Khovanov TQFT with basepoint actions is invariant under connected sum with RP²(-2), vanishes for RP²(+2), answers a Lipshitz-Sarkar question, and yields functoriality for pointed Khovanov homology.