On definite lattices bounded by integer surgeries along knots with slice genus at most 2

We classify the positive definite intersection forms that arise from smooth 4-manifolds with torsion-free homology bounded by positive integer surgeries on the right-handed trefoil. A similar, slightly less complete classification is given for the (2,5)-torus knot, and analogous results are obtained for integer surgeries on knots of slice genus at most two. The proofs use input from Yang–Mills instanton gauge theory and Heegaard Floer correction terms.