K-theory

In mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It also has some applications in operator algebras. It leads to the construction of families of K-functors, which contain useful but often hard-to-compute information.