On the group of homotopy classes of relative homotopy automorphisms

TL;DR

This paper proves that the group of homotopy classes of relative homotopy automorphisms of a simply connected finite CW-complex is finitely presented and that its rationalization map has a finite kernel.

Contribution

It establishes finiteness properties of the group of relative homotopy automorphisms and analyzes the rationalization map's kernel.

Findings

The group is finitely presented.

The rationalization map has a finite kernel.

Provides structural insights into homotopy automorphisms.

Abstract

We prove that the group of homotopy classes of relative homotopy automorphisms of a simply connected finite CW-complex is finitely presented and that the rationalization map from this group to its rational analogue has a finite kernel.