A universal smoothing of four-space
type: Item
instance of: scholarly article
title: A universal smoothing of four-space
zbMATH Open document ID: 0586.57007
author: Laurence R. Taylor
author: Michael Freedman
published in: Journal of Differential Geometry
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R10
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57Q45
Mathematics Subject Classification ID: 57R80
Mathematics Subject Classification ID: 57R55
zbMATH DE Number: 3940270
zbMATH Keywords: smoothly knotted 2-spheres in universal \(R^ 4\)
zbMATH Keywords: smoothing of four space
zbMATH Keywords: smoothing of half space
zbMATH Keywords: h-cobordism between two four-manifolds
zbMATH Keywords: topologically unknotted
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214440258
OpenAlex ID: W2136327844
Wikidata QID: Q107485819
DOI: 10.4310/JDG/1214440258
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description: scientific article; zbMATH DE number 3940270