Kobayashi, Shoshichi; Shinozaki, Eriko Conjugate connections and moduli spaces of connections. (English) Zbl 0893.53008 Tokyo J. Math. 20, No. 1, 67-72 (1997). Let \(G\) be a Lie group and \(H\) a closed subgroup, where \(\operatorname{Aut}(G,H)\) 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 \(\operatorname{Aut}(G, H)/\text{Inn}(G, H)\) acts on the moduli space \({\mathcal C}(P)/{\mathcal G}(P)\), and the action is free on the generic part of \({\mathcal C}(P)/{\mathcal G}(P)\). Reviewer: J.Muciño-Raymundo (Morelia) Cited in 1 ReviewCited in 1 Document MSC: 53C05 Connections (general theory) 58D27 Moduli problems for differential geometric structures Keywords:space of connections; gauge transformations PDFBibTeX XMLCite \textit{S. Kobayashi} and \textit{E. Shinozaki}, Tokyo J. Math. 20, No. 1, 67--72 (1997; Zbl 0893.53008) Full Text: DOI