Geodesic
Algebraic models for homotopy types
Homology, homotopy, and applications, Tome 7 (2005) no. 2, pp. 139-160.

Voir la notice de l'article provenant de la source International Press of Boston

The classical problem of algebraic models for homotopy types is precisely stated here in terms of our ability to compute with the models. Two different natural statements for this problem are produced, the simplest one being entirely solved by the notion of $\mathcal{SS_{EH}}$-structure, due to the authors. Other tentative solutions, Postnikov towers and $E_{\infty}$-chain complexes, are considered and compared with the $\mathcal{SS_{EH}}$-structures. In particular, an imprecision in the usual definition of the $k$-“invariants” is explained, which implies we seem far from a solution for the ideal statement of our problem. On the positive side, the problem stated below in the framed quotation is solved.
DOI : 10.4310/HHA.2005.v7.n2.a8
Classification : 55P15, 18G40, 18G55, 55S45
Keywords: classification, homotopy type, Postnikov system, k-invariant, computable model, algebraic model, computability 
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Julio Rubio; Francis Sergeraert. Algebraic models for homotopy types. Homology, homotopy, and applications, Tome 7 (2005) no. 2, pp. 139-160. doi : 10.4310/HHA.2005.v7.n2.a8. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2005.v7.n2.a8/

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