Some Computational 4-Manifold Topology

Dimension 4 is the first dimension in which exotic smooth manifold pairs appear — manifolds which are topologically the same but for which there is no smooth deformation of one into the other. On the other hand, smooth and PL manifolds (manifolds which can be described discretely) do coincide in dimension 4. Despite this, there has been comparatively little work done towards gaining an understanding of smooth 4-manifolds from the discrete and algorithmic perspective. The aim of this talk will be to give a gentle introduction to some of the tools, techniques, and ideas, which inform a computational approach to 4-manifold topology.