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Conjugate connections and moduli spaces of connections. (English) Zbl 0893.53008

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 \({\mathcal C}(P)/{\mathcal G}(P)\).

MSC:

53C05 Connections (general theory)
58D27 Moduli problems for differential geometric structures
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