A \(G\)-minimal model for principal \(G\)-bundles (Q1166159)

Sullivan associated a uniquely determined \(\text{DGA}\big| _{\mathbb Q}\) to any simply connected simplicial complex \(E\). This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space \(E\). In case \(E\) is the total space of a principal \(G\)-bundle, (\(G\) is a compact connected Lie group) we associate a \(G\)-equivariant model \(\mu_G[E]\), which is a collection of ``\(G\)-homotopic'' DGA's\(\big| _{\mathbb R}\) with \(G\)-action. \(\mu_G[E]\) will, in general, be different from the Sullivan's minimal model of the space \(E\). \(\mu_G[E]\) contains the total rational homotopy information of the spaces \(E\), \(E/G\) and, in addition, it incorporates the action of \(G\) (on \(E\)).