Editing Connection (principal bundle) (section)

=== Computational remarks ===
Most known non-trivial computations of principal ''<math>G</math>''-connections are done with [[homogeneous space]]s because of the triviality of the (co)tangent bundle. (For example, let <math>G \to H \to H/G</math>, be a principal ''<math>G</math>''-bundle over <math> H/G</math>.) This means that 1-forms on the total space are canonically isomorphic to <math>C^\infty(H,\mathfrak{g}^*)</math>, where <math> \mathfrak{g}^*</math> is the dual lie algebra, hence ''<math>G</math>''-connections are in bijection with <math>C^\infty(H,\mathfrak{g}^*\otimes \mathfrak{g})^G</math>.