The Algebra & Geometry of Modern Physics

During the lecture, we will be dealing with a smooth action of a Lie group on a smooth manifold. Our goal is a theorem which states that under additional assumptions on the action (it must be proper and free) there exists only one smooth manifold structure on the space of orbits such that the quotient map M -> M/G is a submersion. We will also prove some additional results concerning manifolds in general and those with a group action.