The lens space realization problem

We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere.Specifically, if surgery along a knot produces a lens space, then there exists an equivalent surgery along a Berge knot with the same knot Floer homology groups.This leads to sharp information about the genus of such a knot.The arguments rely on tools from Floer homology and lattice theory.They are primarily combinatorial in nature.