# On the homotopy type of a chain algebra

## Mahmoud Benkhalifa

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\$.

Homology, Homotopy and Applications, Vol. 6(2004), No. 1, pp. 109-135

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