Conjugate connections and moduli spaces of connections
type: Item
instance of: scholarly article
title: Conjugate connections and moduli spaces of connections
zbMATH Open document ID: 0893.53008
author: Shoshichi Kobayashi
author: Eriko Shinozaki
published in: Tokyo Journal of Mathematics
publication date: 1997-01-01T00:00:00Z
review text: Let \(G\) be a Lie group and \(H\) a closed subgroup, where \(\Aut(G,H)\) is the group of automorphisms of \(G\) leaving all elements of \(H\) fixed, and \(\text{Inn}(G, H)\) its normal subgroup consisting of inner automorphisms. Given a principal \(G\)-bundle \(P\), let \({\mathcal C}(P)\) be the space of connections in \(P\) and \({\mathcal G}(P)\) the group of gauge transformations. The paper shows that, if the structure group \(G\) of \(P\) can be reduced to \(H\), then the group \(\Aut(G, H)/\text{Inn}(G, H)\) acts on the moduli space \({\mathcal C}(P)/{\mathcal G}(P)\), and the action is free on the generic part of \({\mathcal C}(P)/{\mathcal G}(P)\).
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 58D27
zbMATH DE Number: 1054592
zbMATH Keywords: space of connections
zbMATH Keywords: gauge transformations
reviewed by: Jesus Muciño Raymundo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270042400
OpenAlex ID: W2082346969
DOI: 10.3836/TJM/1270042400
description: scientific article; zbMATH DE number 1054592