2-Dimensional Topological Field Theory

A 2-dimensional topological field theory is a mathematical framework that studies properties of surfaces—like disks or spheres—by focusing on their intrinsic shapes and connections, rather than precise measurements. It assigns algebraic data (such as numbers or algebraic structures) to these surfaces and their boundaries, capturing how they can be combined or deformed without changing their fundamental nature. This approach helps understand global properties and relationships in geometry and physics, especially in areas like string theory and condensed matter, where the focus is on how the shape and connectivity influence behavior, regardless of specific distances or angles.