Integer surgeries rational homology cobordant to lens spaces

This talk is about a project that investigates when positive integer surgery on a knot in S^3 is smoothly rational homology cobordant to a lens space. This merges two classic areas of low-dimensional topology together: The study of lens space surgeries, and the study of cobordism. We give a complete answer to what lens spaces can be obtained this way, and some results on surgery slopes. Various tools are involved, including Greene’s changemaker lattice coming from Heegaard Floer d-invariant.