On definite lattices bounded by a homology 3–sphere and Yang–Mills instanton Floer theory

Using instanton Floer theory, extending methods due to Frøyshov, we determine the definite lattices that arise from smooth 4-manifolds bounded by certain homology 3-spheres.For example, we show that for +1 surgery on the (2,5) torus knot, the only non-diagonal lattices that can occur are E8 and the indecomposable unimodular definite lattice of rank 12, up to diagonal summands.We require that our 4-manifolds have no 2-torsion in their homology.