Algebraic models for homotopy types.
- Rubio, J. 1
- Sergeraert, F. 2
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1
Universidad de La Rioja
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2
Joseph Fourier University
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ISSN: 1532-0073
Year of publication: 2005
Volume: 7
Issue: 2
Pages: 139-160
Type: Article
More publications in: Homology, Homotopy and Applications
Abstract
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 SSEH-structure, due to the authors. Other tentative solutions, Postnikov towers and E∞-chain complexes, are considered and compared with the SSEH-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.