## Knotted Surfaces in 4-manifolds and Distances Between Them

Oliver Singh (Durham)

Abstract

I will discuss knotted surfaces, isotopy classes of embedded surfaces in a given 4-manifold, and will define two notions of distance between them. These distances are integer-valued and are defined topologically: one in terms of regular homotopy; another in terms of stabilisation, a form of embedded surgery. I will outline a proof of an inequality between these distances; the proof is constructive and draws upon ideas pioneered by Gabai in the proof of the 4-dimensional light bulb theorem.