Surgery in cusp neighborhoods and the geography of irreducible 4-manifolds
type: Item
instance of: scholarly article
title: Surgery in cusp neighborhoods and the geography of irreducible 4-manifolds
zbMATH Open document ID: 0843.57021
DOI: 10.1007/BF01232253
author: Ronald Fintushel
author: Ronald Stern
published in: Inventiones Mathematicae
publication date: 1996-08-18T00:00:00Z
full work available at URL: https://eudml.org/doc/144224
review text: The longstanding conjecture that every smooth simply-connected 4-manifold is the connected sum of complex surfaces was recently disproved by Gompf and Mrowka. They constructed infinite families of such 4-manifolds which are homeomorphic to the K3 surface but admit no complex structure. In the same spirit, the authors of this paper provide infinite families of irreducible noncomplex 4-manifolds homotopy equivalent to minimal elliptic surfaces respectively various classes of surfaces of general type. These examples are then combined to obtain simply connected irreducible 4-manifolds which are not homotopy equivalent to any complex surface.
reviewed by: Peter Teichner
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 703858
zbMATH Keywords: 4-manifolds
zbMATH Keywords: cusps
zbMATH Keywords: gauge theory
zbMATH Keywords: complex surfaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 703858