Julio Rubio, Francis Sergeraert
The very nature of the so-called Postnikov invariants is carefully studied. Two functors, precisely defined, explain the exact nature of the connection between the category of topological spaces and the category of Postnikov towers. On one hand, these functors are in particular effective and lead to concrete machine computations through the general machine program Kenzo. On the other hand, the Postnikov "invariants" will be actual invariants only when an arithmetical decision problem - currently open - will be solved; it is even possible this problem is undecidable.
Algebraic topology, Postnikov invariants, k-invariants, homotopy type, classification.
MSC 2000: 55P15, 55S45, 55U40, 55-04