Equivariant cohomology

Equivariant cohomology is a mathematical framework that studies shapes or spaces that have symmetries, represented by a group action (like rotating or reflecting). It combines traditional cohomology, which captures the shape's structure, with information about these symmetries. This allows mathematicians to analyze how the shape's properties are affected by symmetry, providing a richer understanding of spaces that are symmetric under certain transformations. Essentially, it extends the concept of measuring a space’s features to include how those features behave under specific symmetries.