The Whitehead exact sequence and the classification problem of homotopy types

TL;DR

This paper introduces a new, simpler invariant related to Whitehead's exact sequence that can classify homotopy types of simply connected CW-complexes in favorable cases, offering a more elementary approach than previous methods.

Contribution

It defines a less powerful but more elementary invariant associated with Whitehead's exact sequence that can classify homotopy types in certain cases.

Findings

The invariant is simpler than Baues' boundary invariant.

It successfully classifies homotopy types in good cases.

Provides a new approach to the classification problem.

Abstract

This paper defines an invariant associated to Whitehead's certain exact sequence of a simply connected CW-complex which is much more elementary - and less powerful - than the boundary invariant of Baues. Nevertheless, in good cases, it classifies the homotopy types of CW-complexes.