Two links at one point: an illustrated companion to the construction

Abstract

This companion explains the construction in Topological singularities in the codimension-two stratum of noncollapsed Ricci limits. The fixed manifold recording the topology of a punctured neighbourhood differs from the limiting link determining its metric tangent. We follow this distinction through the actual edge regularization, the construction of caps with prescribed boundary tensors, the uniform parameter choices, and the two volume normalizations. We then explain the radial curvature estimates, the comparison of ambient distances, and the exact smooth filling procedure. The local homology calculation identifies the obstruction to a manifold chart, although the neighbourhood is contractible and the unique metric tangent is topologically Euclidean.