Basic Algebraic Topology

Chapter 9 Cohomology of Sheaves

The concept of sheaves has its origin in the study of holomorphic functions on a complex manifold. It provides a systematic approach to keep track of local algebraic data on a topological space and aids in arriving at global conclusions. Experience has shown that certain techniques developed in dealing with holomorphic functions are applicable to smooth functions, continuous functions, and so on. Sheaf theory is the outcome of axiomatizing certain basic local properties common to all these functions. In this chapter, we shall present some basic properties of sheaves. For further reading one may look into [Ramanan, 2004].

In Section 9.1, we discuss some generalities about presheaves and sheaves. In Section 9.2 ...