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We classify all the lattices realized as the intersection form of a positive definite four manifold with boundary Sₙ³ (K) for a knot K in the three sphere and a positive integer n greater than 4g₄ (K) +3. We then use this result to define a concordance invariant and generalize a theorem of Rasmussen on lens space surgeries.
Ali Naseri Sadr (Mon,) studied this question.