Polar manifolds and actions

A group action is called polar if there exists an immersed submanifold (a section) which intersects all orbits orthogonally. We show how to construct a manifold admitting a polar group action by prescribing its isotropy groups along a fundamental domain in the section. This generalizes a classical construction for cohomogeneity-one manifolds.We give many examples showing the richness of this class of group actions and relate the topology of the section to the topology of the manifold.