Sheaf cohomology

Sheaf cohomology is a mathematical tool used to analyze how local data—like functions, solutions, or properties—assembled over small regions, extend and interact across an entire space. It helps identify global features arising from local information, detecting obstructions to stitching local solutions into a consistent whole. Essentially, it provides a systematic way to measure the differences between local patterns and their capacity to form a unified global picture, offering insights into the structure and properties of complex spaces in geometry and topology.