turkmath.org

The theory of foliations is a wide field of research having both quantitative and qualitative aspects. Intuitively, a foliation on a manifold corresponds to a partition of the manifold into connected, immersed submanifolds of the same dimension, called leaves which form locally layers of a Euclidean space. Existence problem of foliations on closed manifolds is solved in 1970’s by W. Thurston as the culmination of efforts of several mathematicians. However, not much is known about the existence problem of equivariant foliations (i.e. the foliations whose leaves are invariant under a group action on the manifold). In this talk for a general audience, we will first review some basic notions about the foliations, and then will present some results about the existence of equivariant foliations on spheres.