Embeddings of surfaces in 4-manifolds. I
type: Item
instance of: scholarly article
title: Embeddings of surfaces in 4-manifolds. I
zbMATH Open document ID: 0764.57021
DOI: 10.1007/BF02882940
published in: Chinese Science Bulletin
publication date: 1993-01-17T00:00:00Z
review text: The author applies Donaldson's result on the nonexistence of certain unimodular forms as intersection forms of smooth 4-manifolds to the problem of representing 2-dimensional homology classes of smooth simply connected 4-manifolds by embedded 2-spheres. He obtains new and complete results in the case of the connected sum of two or three copies of \(S^ 2\times S^ 2\) or the nontrivial \(S^ 2\)-bundle over \(S^ 2\). He also studies the problem which Euler numbers can occur for the normal bundle of an embedding of \(\mathbb{R} P^ 2\) (resp. the Klein bottle). New and complete results are obtained for some special 4-manifolds like \(S^ 2\times S^ 2\) or the nontrivial \(S^ 2\)-bundle over \(S^ 2\). [Part II is reviewed below (see Zbl 0764.57022)].
Mathematics Subject Classification ID: 57R95
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R40
zbMATH DE Number: 96618
zbMATH Keywords: nonexistence of unimodular forms as intersection forms of smooth 4- manifolds
zbMATH Keywords: representing 2-dimensional homology classes of smooth simply connected 4-manifolds by embedded 2-spheres
zbMATH Keywords: Euler numbers
zbMATH Keywords: normal bundle of an embedding of \(\mathbb{R} P^ 2\)
zbMATH Keywords: Klein bottle
author: Bang-He Li
reviewed by: Peter Teichner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 96618