Chern–Connes character

Summary

The Chern–Connes character is a homomorphism from the K-theory of an algebra to its cyclic homology. It sends the class of an idempotent matrix to the class of a cyclic cycle built from the idempotent. It extends the classical Chern character of vector bundles to noncommutative algebras, and it is a basic tool of noncommutative geometry.