cohomology ring

A cohomology ring is a mathematical structure that captures how different features of a space (like holes or twists) relate and combine. Think of it as a catalog that records the ways you can measure these features and how these measurements interact when combined. It organizes this information using algebraic rules, allowing mathematicians to understand the shape's shape and structure in a systematic way. Essentially, it provides a powerful language for studying the global properties of spaces, revealing insights that are foundational in topology and geometry.