Topological classification of 4-dimensional complete intersections
type: Item
instance of: scholarly article
title: Topological classification of 4-dimensional complete intersections
zbMATH Open document ID: 0866.57015
DOI: 10.1007/BF02568299
author: Stephan Klaus
author: Fuquan Fang
published in: Manuscripta Mathematica
publication date: 1997-07-20T00:00:00Z
full work available at URL: https://eudml.org/doc/156187
review text: The main result of the paper is: Two 4-dimensional complete intersections of a complex projective space are homeomorphic if and only if they have the same total degree, Pontryagin numbers and Euler number. For dimension 1 and 3 the diffeomorphism classification is well known by surface theory and the classification of 1-connected 6-manifolds [\textit{A. V. Zhubr}, Math. USSR, Izv. 9(1975), 793-812 (1976); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 39, 839-859 (1975; Zbl 0318.57019)], for dimension 2 the topological classification is known by M. Freedman's results. For higher dimensions it is still open. In fact, the authors classify certain more general 1-connected 8-manifolds using bordism structure. Remark: The numbers mentioned in the Theorem are computed from the total Chern class, not in the paper but presented there.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 922471
zbMATH Keywords: complete intersections
zbMATH Keywords: complex projective space
zbMATH Keywords: homeomorphic
zbMATH Keywords: degree
zbMATH Keywords: Pontryagin numbers
zbMATH Keywords: Euler number
reviewed by: Konrad Drechsler
MaRDI profile type: Publication
cites work: Q5649690
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description: scientific article; zbMATH DE number 922471