**Julio Rubio, Francis Sergeraert**

## Postnikov "Invariants" in 2004

**Abstract:**

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.

**Keywords:**

Algebraic topology, Postnikov invariants, k-invariants, homotopy type,
classification.

**MSC 2000:** 55P15, 55S45, 55U40, 55-04