Rigidity of Fibering

Given a manifold M, it is natural to ask in how many ways it fibers (we mean fibering in a general way, where the base might be an orbifold – this could be described as Seifert fibering)There are group-theoretic obstructions to the existence of even one fibering, and in some cases (such as Kahler manifolds or three-dimensional manifolds) the question reduces to a group-theoretic question. In this note we summarize the author’s state of knowledge of the subject.