On definite lattices bounded by integer surgeries along knots with slice genus at most 2
arXiv:1807.11931
Abstract
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.
20 pages, 6 figures; final version, to appear in the Transactions of the AMS