Constructible Sheaves, Vanishing Cycles and Characteristic Varieties

Constructible sheaves and constructible functions, objects in which algebra and topology are blended in subtle way, are introduced in the first section. The study of the variation in the topology of the fibers of a function is encoded in two functors, the nearby cycles and the vanishing cycles, whose definitions and main properties are given in the second section. The characteristic variety and the characteristic cycle, geometric ways to measure how far a constructible sheaf is from a local system, are introduced in the third section.