Event description
Abstract: If a Lie group G acts properly on a manifold M, then there exists a subgroup H and an H-invariant submanifold N, called the core, such that the quotient M/G is isometric to the quotient N/H. In this talk we introduce some basic facts of proper group actions on smooth manifolds and show the construction of the core. We define the notion of a polar action and show that the G-action on M is polar if and only if the H-action on N is polar, i.e. we prove that there is a reduction principle for polar actions. This is a joint work with Leonardo Biliotti and Alessandro Minuzzo.