Cyclic homology

Summary

Cyclic homology is a homology theory for associative algebras introduced by Alain Connes and, independently, by Boris Tsygan. It refines Hochschild homology by taking into account the cyclic rotation of tensor factors. For smooth commutative algebras in characteristic $0$ it is computed from de Rham cohomology. So it plays the role of de Rham theory in noncommutative geometry. It is also the target of trace maps from algebraic K-theory.