The Künneth formula in cyclic homology (Q1082429)

The cyclic homology of a cyclic module G (i.e. a simplicial module with additional structure) can be computed from an ''algebraic \(S^ 1\)-chain complex'' \(\tilde C(G)\) (i.e. a chain complex with additional structure). The authors show that if G and G' are cyclic modules then \(\tilde C(G\otimes G')\) and \(\tilde C(G)\otimes \tilde C(G')\) have the same cyclic homology. They derive a Künneth formula for the cyclic homology of algebras; as an application, they compute the cyclic homology of polynomial and Laurent algebras.