Freedman, Michael H.; Taylor, Laurence R. A universal smoothing of four-space. (English) Zbl 0586.57007 J. Differ. Geom. 24, 69-78 (1986). 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. Cited in 1 ReviewCited in 9 Documents MSC: 57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) 57R10 Smoothing in differential topology 57R40 Embeddings in differential topology 57Q45 Knots and links in high dimensions (PL-topology) (MSC2010) 57R80 \(h\)- and \(s\)-cobordism 57R55 Differentiable structures in differential topology Keywords:smoothly knotted 2-spheres in universal \(R^ 4\); smoothing of four space; smoothing of half space; h-cobordism between two four-manifolds; topologically unknotted PDFBibTeX XMLCite \textit{M. H. Freedman} and \textit{L. R. Taylor}, J. Differ. Geom. 24, 69--78 (1986; Zbl 0586.57007) Full Text: DOI