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We give a purely combinatorial proof of the K\"{u}nneth formula for the knotFloer homology of connected sums by constructing a quasi-isomorphism of gridchain complexes. This proof is complete within the framework of the knot gridhomology. The construction of the quasi-isomorphism naturally deduces that theLegendrian and transverse invariants behave functorially with respect to theconnected sum operation.

Quasi-isomorphism of grid chain complexes for a connected sum of knots