A universal smoothing of four-space
The authors construct a smoothing of four space into which all other smoothings of four space smoothly imbed. This is the universal smoothing of the title. The key step in the construction is to manufacture a smoothing of half space, \(H^ 4\). This half space has the following property. Suppose we have a smooth, proper h-cobordism between two four- manifolds, each with one end. Suppose each four manifold has a copy of \(H^ 4\) properly smoothly imbedded in it. Then the h-cobordism is a smooth product iff it is a topological one. There are several applications of this result presented in addition to the construction of a universal smoothing of four-space. As one example, the authors classify all smoothly knotted 2-spheres in their universal \({\mathbb{R}}^ 4\) which are topologically unknotted. There are the expected two.
smoothly knotted 2-spheres in universal \(R^ 4\)
scientific article; zbMATH DE number 3940270