singular cohomology

Singular cohomology is a mathematical tool used to study the shape and structure of spaces. It assigns algebraic objects, such as groups, to a space, capturing information about features like holes or voids of different dimensions. By analyzing these groups, mathematicians can classify and distinguish shapes based on their topological properties, regardless of how they are stretched or deformed, as long as they aren’t torn or glued. Singular cohomology thus provides a rigorous way to understand the global geometric features of complex shapes through algebraic means.