Irreducible four-manifolds with small Euler characteristics
type: Item
instance of: scholarly article
title: Irreducible four-manifolds with small Euler characteristics
zbMATH Open document ID: 0874.57022
DOI: 10.1016/0040-9383(95)00014-3
author: Zoltán Szabó
published in: Topology
publication date: 1997-11-09T00:00:00Z
review text: The author investigates two smooth, closed, simply-connected 4-manifolds \(Q\) and \(R\) constructed by \textit{Gompf} [``A new construction of symplectic manifolds'', preprint)] that are topologically \(3\mathbb{C}\mathbb{P}^2\# 16\mathbb{C}\mathbb{P}^2\) and \(3\mathbb{C}\mathbb{P}^2\# 14\mathbb{C}\mathbb{P}^2\). With the standard smooth structure all Donaldson invariants vanish; the author shows however that with the given structure \(Q\) and \(R\) have some non-vanishing SO(3) Donaldson invariants. This is shown by first establishing a Floer-type product formula. He then constructs two families of simply connected closed mutually non-diffeomorphic 4-manifolds \(Q_{2n+1}\) and \(R_{2n+1}\) of the same homeomorphism type of \(Q\) and \(R\) respectively.
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 878550
zbMATH Keywords: 4-manifolds
zbMATH Keywords: Donaldson invariants
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
full work available at URL: 0040-9383(95)00014-3
OpenAlex ID: W1988118679
Recommended article: Q4351000
Recommended article: Irreducible 4-manifolds with abelian non-cyclic fundamental group of small rank
Recommended article: Minimal Euler characteristics of 4-manifolds with 3-manifold groups
Recommended article: On the signature and Euler characteristic of certain four-manifolds
Recommended article: The Euler Characteristic of a Haken 4-Manifold
Recommended article: Minimizing Euler characteristics of symplectic four-manifolds
Recommended article: Small exotic 4-manifolds
Recommended article: Aspherical 4-manifolds of odd Euler characteristic
Recommended article: The geography of irreducible 4-manifolds
Recommended article: Minimal Euler characteristics for even-dimensional manifolds with finite fundamental group
description: scientific article; zbMATH DE number 878550