On the number of non-equivalent differentiable structures on 4-manifolds
type: Item
instance of: scholarly article
title: On the number of non-equivalent differentiable structures on 4-manifolds
zbMATH Open document ID: 0682.14026
DOI: 10.1007/BF01168869
author: Mario Salvetti
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155374
review text: Recently, by virtue of Donaldson's new invariant, it became possible to construct some algebraic surfaces which are homeomorphic to each other, but not diffeomorphic. The author considers some iterated cyclic coverings of \({\mathbb{P}}^ 2\) so that he could construct such surfaces which are simply connected. He also shows that, for any given value of k, his method realizes k distinct differentiable structures (as complex surfaces) on a single topological 4-manifold. So this implies that the moduli spaces of surfaces with given numerical characters can have arbitrary many connected components.
reviewed by: Eiji Horikawa
Mathematics Subject Classification ID: 14J15
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 32J25
zbMATH DE Number: 4116703
zbMATH Keywords: Donaldson invariant
zbMATH Keywords: iterated cyclic coverings
zbMATH Keywords: topological 4-manifold
zbMATH Keywords: moduli spaces of surfaces
MaRDI profile type: Publication
cites work: Q3739261
cites work: On the moduli spaces of surfaces of general type. Appendix: Letter of E. Bombieri written to the author
cites work: Q4723879
cites work: Connected components of moduli spaces
cites work: The topology of four-dimensional manifolds
cites work: On the 𝐶^{∞} invariance of the canonical classes of certain algebraic surfaces
cites work: Analogs of Lefschetz theorems for linear systems with isolated singularities
description: scientific article; zbMATH DE number 4116703