Connection with cyclic homology

Abstract

In this section we expose a brief survey of the natural relationship of algebraic K-theory with cyclic homology which can be viewed as an “additive” algebraic K-theory, the linear group being replaced by the Lie algebra of matrices. The cyclic homology is also closely related to Hochschild homology and de Rham cohomology. Waldhausen’s algebraic A-theory of a simply connected space X can be computed rationally from the cyclic homology of the minimal model of X. There are defined also characteristic classes from algebraic K-theory to cyclic homology.