On the homotopy type of a chain algebra

Abstract

Let $R$ be a P.I.D and let $A$ be a dga over $R$. It is well-known that the graded homology modules $H_{\ast }(A)$ and $% Tor_{\ast }^{A}(R,R)$ alone do not suffice (in general) to determine the homotopy type of the dga $A$. J.H. Baues had built a more precise invariant, the "certain" exact sequence of Whitehead associated with $A.$ Whitehead had built it for CW-complexes. In this work we explore this sequence to show how it can be used to classify the homotopy types of $A$.