Can one classify finite Postnikov pieces?

TL;DR

This paper compares classical and global methods for classifying finite Postnikov pieces, focusing on 3-stage cases, and discusses the computational challenges involved in both approaches.

Contribution

It provides a detailed comparison of classical and global classification methods for finite Postnikov pieces, highlighting cases where classification is feasible.

Findings

Classification is feasible for certain 3-stage Postnikov pieces.

Computational difficulty of global approach is comparable to classical methods.

Examples illustrate the practical aspects of classification.

Abstract

We compare the classical approach of constructing finite Postnikov systems by k-invariants and the global approach of Dwyer, Kan, and Smith. We concentrate on the case of 3-stage Postnikov pieces and provide examples where a classification is feasible. In general though the computational difficulty of the global approach is equivalent to that of the classical one.