Particles and connections on four-manifolds
type: Item
instance of: scholarly article
title: Particles and connections on four-manifolds
zbMATH Open document ID: 0963.58005
published in: Communications in Analysis and Geometry
publication date: 2001-06-24T00:00:00Z
review text: The author studies the spaces of gauge equivalence classes of based connections on a principal \(G\)-bundle over a compact four-manifold \(X\). The aim is to build a particle model for these spaces (in the spirit of May Milgram models) so that one gets natural operations in homotopy. To perform this, for a simple and simply connected classical gauge group \(G\), the author builds spaces \(P(X,Y)\) homotopy equivalent to spaces \(B(X,Y)\) of gauge equivalence classes of pairs \((G\)-connections on a four manifold \(X\), trivialisations of the \(G\) bundle over \(Y(X)\)). The space consists of configurations of particle like connections, each corresponding to an instanton over the four sphere. It is related to the Atiyah-Jones conjecture (stated originally for the four sphere) that the inclusion of the moduli space of instantons of charge \(k\) to the space of gauge equivalence classes of connections of charge \(k\) induces a homology equivalence through a range that increases with \(k\). Hence, the models in the paper provide a first step in proving the Atiyah-Jones conjecture.
reviewed by: Jesus Muciño Raymundo
Mathematics Subject Classification ID: 58D27
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 1295153
zbMATH Keywords: \(G\)-bundle
zbMATH Keywords: \(G\)-connections
zbMATH Keywords: four-manifold
zbMATH Keywords: Atiyah-Jones conjecture
author: Jacques Hurtubise
MaRDI profile type: Publication
full work available at URL: cag.1999.v7.n1.a2
OpenAlex ID: W2737650048
DOI: 10.4310/CAG.1999.V7.N1.A2
description: scientific article; zbMATH DE number 1295153