A structure theorem and a splitting theorem for simply-connected smooth 4-manifolds
This well-written paper provides an improvement of a result of Freedman and Taylor on splitting a 4-manifold \(M\) into two parts associated to an orthogonal splitting of its intersection pairing. In the case when \(M\) is simply connected and \((H_2(M;Z),q) = (Z^{n_1}, q_1) + (Z^{n_2},q_2)\), the new version asserts not only that \(M\) can be decomposed into a union of two submanifolds \(M_1\), \(M_2\) along a homology 3-sphere with \(H_2(M_i;Z) = (Z^{n_i}, q_i)\), but in addition that these submanifolds \(M_i\) can be made simply connected. This fundamental result should be compared with the recent work of \textit{C. L. Curtis}, \textit{M. H. Freedman}, \textit{W. C. Hsiang} and the author [Invent. Math. 123, 343-348 (1996; Zbl 0843.57020)]. From a technical viewpoint, the main advance by the author is contained in his Theorem 2 which shows a simply connected 4-manifold has a handlebody structure with 2-handles homotopically cancelling out both the 1-handles and dual 1-handles in the nicest possible way!
scientific article; zbMATH DE number 817770