A structure theorem and a splitting theorem for simply-connected smooth 4-manifolds
type: Item
instance of: scholarly article
title: A structure theorem and a splitting theorem for simply-connected smooth 4-manifolds
zbMATH Open document ID: 0858.57024
published in: Mathematical Research Letters
publication date: 1996-01-08T00:00:00Z
review text: 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!
reviewed by: R. Lee
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 817770
zbMATH Keywords: splitting
zbMATH Keywords: 4-manifold
zbMATH Keywords: intersection pairing
zbMATH Keywords: homology 3-sphere
zbMATH Keywords: handlebody
author: Richard A. Stong
MaRDI profile type: Publication
DOI: 10.4310/MRL.1995.V2.N4.A9
description: scientific article; zbMATH DE number 817770