Optimal Orbit Reduction

As we already pointed out the main difference between the point and orbit reduced spaces is the invariance properties of the submanifolds out of which they are constructed. More specifically, if we mimic in the optimal context the standard orbit reduction procedure, the optimal orbit reduced space that we should study is G · J⁻¹(ρ)/G = J⁻¹(O _ρ )/G, where O _ρ  := G· ⊂ M/Aʹ _G . The following pages constitute an in-depth study of this quotient and its relation with new (pre)-symplectic manifolds that can be used to reproduce the classical orbit reduction program and expressions.