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.
Baldwin, Adam Simon Levine, and Sucharit Sarkar, K hovanov homology and knot F loer homology for pointed links , J
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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.