turkmath.org

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. An almost complex foliation is a foliation whose tangent bundle admits a complex structure. The existence problem of foliations on closed manifolds is reduced to the existence problem of plane fields in 1970’s by W. Thurston which can be attacked by algebraic topological methods. However, not much has been written about the existence problem of almost complex foliations. On spheres, İ. Dibağ’s results provide concrete necessary conditions in terms of the dimension of the sphere and the dimension of the foliation. In this talk, after reviewing some basic notions about the foliations, we will present some results in the other direction, i.e. about the sufficient conditions for the existence of almost complex foliations on spheres.