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# Homology, Homotopy and Applications

## Volume 6 (2004)

### Number 1

### On the homotopy type of a chain algebra

Pages: 109 – 135

DOI: http://dx.doi.org/10.4310/HHA.2004.v6.n1.a8

#### Author

#### 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 $A$.

#### Keywords

differential graded algebra, Whitehead exact sequence, Detecting functor, Homotopy type

#### 2010 Mathematics Subject Classification

55Q15, 55U40