On the intersection forms of closed 4-manifolds
type: Item
instance of: scholarly article
title: On the intersection forms of closed 4-manifolds
zbMATH Open document ID: 0779.57012
DOI: 10.5565/PUBLMAT_36192_07
author: Friedrich Hegenbarth
author: Alberto Cavicchioli
published in: Publicacions Matemàtiques
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/41166
review text: The authors study how the intersection form of a PL 4-manifold changes under a sequence of surgeries on curves that yield a simply connected manifold \(M^*\). The focus is on the case when the surgeries are on elements of finite order, with the result in this case being that the surgery adds copies of either \(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\) or \(\begin{pmatrix} 1 & 0 \\ 0 & -1\end{pmatrix}\) to the intersection form. Results of Donaldson and Freedman are then applied to determine the homeomorphism type of \(M^*\) under various hypotheses.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 94208
zbMATH Keywords: intersection form of a PL 4-manifold
zbMATH Keywords: surgeries on curves
zbMATH Keywords: homeomorphism type
reviewed by: Terry Lawson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 94208