Cohomological field theory

Cohomological field theory is a mathematical framework that studies spaces and their properties using tools from quantum field theory. It assigns algebraic invariants—called cohomology classes—to geometric objects, capturing their shape, structure, and symmetries. This approach allows mathematicians to analyze complex geometric spaces by translating geometric questions into algebraic problems, often revealing deep relationships between topology, geometry, and physics. Essentially, it provides a way to systematically understand and categorize high-dimensional spaces through concepts inspired by physics, leading to insights across mathematics and theoretical physics.