Embeddings of surfaces in 4-manifolds. I
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)].
nonexistence of unimodular forms as intersection forms of smooth 4- manifolds
representing 2-dimensional homology classes of smooth simply connected 4-manifolds by embedded 2-spheres
normal bundle of an embedding of \(\mathbb{R} P^ 2\)
scientific article; zbMATH DE number 96618
scientific article