Classification of closed oriented 4-manifolds modulo connected sum with simply connected manifolds
type: Item
instance of: scholarly article
title: Classification of closed oriented 4-manifolds modulo connected sum with simply connected manifolds
zbMATH Open document ID: 0911.57016
author: Ichiji Kurazono
author: Takao Matumoto
published in: Hiroshima Mathematical Journal
publication date: 1999-05-04T00:00:00Z
review text: Two closed oriented 4-manifolds \(M\) and \(N\) are said to be stably equivalent if there are simply connected closed 4-manifolds \(M_0\) and \(N_0\) such that the connected sums \(M\# M_0\) and \(N\# N_0\) are orientation preserving homeomorphic. The authors classify the stable equivalence classes of connected oriented 4-manifolds \(M\) with finite presentable fundamental group \(\pi\) showing that they one-to-one correspond to the elements of the quotient \(H_4(B\pi;\mathbb{Z})/\Aut\pi\). The correspondence is given by \(M\to f_*[M]\), where \([M]\) denotes the fundamental class of \(M\), and \(f:M\to B\pi=K (\pi,1)\) is the classifying map. Applications are given for classes of closed 4-manifolds with special fundamental groups.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1216681
zbMATH Keywords: closed four-manifolds
zbMATH Keywords: stable decomposition
zbMATH Keywords: classifying spaces
zbMATH Keywords: connected sums
zbMATH Keywords: stable equivalence
zbMATH Keywords: classifying map
reviewed by: Alberto Cavicchioli
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1216681