On the group of homotopy classes of relative homotopy automorphisms
Hadrien Espic, Bashar Saleh

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Geometric and Algebraic Topology
