simplicial cohomology

Simplicial cohomology is a mathematical tool used to study shapes and spaces by breaking them down into basic building blocks called simplices (points, line segments, triangles, etc.). It captures information about the shape's structure, like holes or voids, by assigning algebraic data to these building blocks. This data, organized in groups called cohomology groups, reveals properties such as connectedness or the presence of holes at various dimensions. Essentially, simplicial cohomology translates geometric features into algebraic forms, allowing for systematic comparison and classification of complex shapes in a precise, mathematical way.