On self-dual pseudo-connections on some orbifolds
type: Item
instance of: scholarly article
title: On self-dual pseudo-connections on some orbifolds
zbMATH Open document ID: 0774.57012
DOI: 10.1007/BF02570838
author: Mikio Furuta
published in: Mathematische Zeitschrift
publication date: 1992-08-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174367
review text: The author adapts the gauge theory developed by \textit{S. Donaldson} for definite 4-manifolds to the study of certain definite 4-dimensional orbifolds whose singularities are cones on lens spaces. As a corollary it is shown that if such an orbifold \(X\) has \(\pi_ i(X)=0\), \(H_ 2(X;Q)=0\), and at least one singularity that is the cone on a lens space \(L(p,1)\) with \(p\neq 4\), then there must be another singularity which is also the cone on \(-L(p,1)\). This in turn implies that if \(L(p,1)\#- L(p',q)\) smoothly embeds in the 4-sphere, then \(L(p',q)\) is diffeomorphic to \(L(p,1)\). Furthermore the author gives a nice proof of \textit{Kuga}'s theorem [Topology 23, 133-137 (1984; Zbl 0551.57019)] about smooth embeddings of \(S^ 2\) into \(S^ 2\times S^ 2\).
reviewed by: R. J. Stern
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 58D19
Mathematics Subject Classification ID: 57R95
Mathematics Subject Classification ID: 58E15
Mathematics Subject Classification ID: 57R57
zbMATH DE Number: 39974
zbMATH Keywords: self-dual connections
zbMATH Keywords: instantons
zbMATH Keywords: definite 4-dimensional orbifolds
zbMATH Keywords: cones on lens spaces
MaRDI profile type: Publication
cites work: Self-duality in four-dimensional Riemannian geometry
cites work: An application of gauge theory to four dimensional topology
cites work: SO(3)-connections and the topology of 4-manifolds
cites work: Pseudofree orbifolds
cites work: Rational homology cobordisms of spherical space forms
cites work: Q5185713
cites work: Q3799340
cites work: Homology cobordism group of homology 3-spheres
cites work: On embedding 3-manifolds in 4-space
cites work: Representing homology classes of \(S^ 2\times S^ 2\)
cites work: The index of elliptic operators over V-manifolds
cites work: Q3730551
cites work: Compactness results for orbifold instantons
cites work: Self-dual Yang-Mills connections on non-self-dual 4-manifolds
cites work: Connections with \(L^ p \)bounds on curvature
cites work: Removable singularities in Yang-Mills fields
OpenAlex ID: W1986298623
description: scientific article; zbMATH DE number 39974