Answering global questions with local data is a common theme in geometry, and sheaves are a powerful tool for organizing such problems. Cech cohomology aids in the study of sheaves on topological spaces, and helps us understand when local data is enough to answer a global question. We will discuss the basics of sheaves, and then go over the construction of Cech cohomology. We will examine basic theorems with an emphasis on motivation, examples, and accessibility. Applications to topology and geometry will also be covered, and so a cursory review of simplicial homology and complex analysis prior to the talk may be useful.
Sheaves and Cech Cohomology