Classification of Lattices Bounded by Large Surgeries of Knots

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.