K-group

K-groups are mathematical tools used in algebraic topology and K-theory to classify and analyze vector bundles and projective modules over a space or algebra. Essentially, they organize complex structural information into algebraic groups, allowing mathematicians to study properties like shape and symmetry in a structured way. These groups capture information about how objects can be combined, compared, or transformed within a given context, providing a powerful framework for understanding geometric and topological features through algebraic means.