Iterated cyclic homology

Abstract

From the viewpoint of rational homotopy theory, we introduce an iterated cyclic homology of connected commutative differential graded algebras over the rational number field, which is regarded as a generalization of the ordinary cyclic homology. Let T be the circle group and $¥mathcal{F}$ (T^l, X) denote the function space of continuous maps from the l-dimensional torus T^l to an l-connected space X. It is also shown that the iterated cyclic homology of the differential graded algebra of polynomial forms on X is isomorphic to the rational cohomology algebra of the Borel space ET × _T $¥mathcal{F}$ (T^l, X), where the T-action on $¥mathcal{F}$ (T^l, X) is induced by the diagonal action of T on the source space T^l.