Low Dimensional Geometry and Topology Special Feature: Topology of surface diagrams of smooth 4-manifolds

摘要

Surface diagrams are a new way to specify any smooth closed orientable 4-manifold by an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each curve has a unique transverse intersection with the next. The aim of this paper is to announce a uniqueness theorem for these objects (within a fixed homotopy class) that turns out to be similar to the Reidemeister-Singer theorem for Heegaard splittings of 3-manifolds.