Homological perturbation theory and computability of Hochschild and cyclic homologies of CDGAs

Abstract

We establish an algorithm computing the homology of commutative differential graded algebras (briefly, CDGAs). The main tool in this approach is given by the Homological Perturbation Theory particularized for the algebra category (see \cite{Rea96a}). Taking into account these results, we develop and refine some methods already known about the computation of the Hochschild and cyclic homologies of CDGAs. In the last section of the paper, we analyze the $p$-local homology of the iterated bar construction of a CDGA ($p$ prime).