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Differentiable structures on punctured 4-manifolds. (English) Zbl 0799.57009

By a result of Quinn, any closed simply-connected 4-manifold becomes smoothable after removing a point. In this paper, the authors give sufficient conditions for such punctured 4-manifolds to have uncountably many differentiable structures. For example, they prove this result if the closed 4-manifold (not necessarily simply-connected) was smooth to begin with or if one introduces two punctures instead of one. This generalizes the famous construction of uncountably many differentiable structures on Euclidean 4-space (which is the punctured 4-sphere).
Reviewer: P.Teichner (Mainz)

MSC:

57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
57R55 Differentiable structures in differential topology
57R57 Applications of global analysis to structures on manifolds
57R10 Smoothing in differential topology
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