Introduction to taut foliations

The existence of a taut foliation on a three-manifold has significant topological and geometric consequences.  In this talk, we will introduce foliations, including several examples, and define the notion of tautness (as well as several equivalent conditions).  To illustrate the usefulness of these constructions, we will sketch a proof of Novikov’s theorem concerning the irreducibility of three-manifolds admitting taut foliations.