The International Conference on
Secondary Calculus and Cohomological Physics,
Moscow, August 24 - August 31, 1997

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

A. Alvarez, J.A. Armario, P. Real, B. Silva

Dpto. Matematica Aplicada I, Univ. de Sevilla E-mails:,,,

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).

Keywords: Homology, CDGA, bar construction, (minimal) homological model, contraction, perturbation, twisted tensor product of CDGA

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