cohomological dimension

Cohomological dimension is a mathematical concept that measures the complexity of a space or a group in terms of how many levels of algebraic information need to be considered to understand its structure. Think of it as the smallest number of steps needed in a process to capture all the essential features of that object using a type of algebraic tools called cohomology. A lower dimension indicates a simpler structure, while a higher dimension suggests more intricate relationships. It helps mathematicians classify and analyze spaces or groups based on their inherent algebraic complexity.