The Group of Self-Homotopy Equivalences of an F₀-Space and the Whitehead Exact Sequence

A simply connected rational CW complex X is called an F 0 -space if it has finitedimensional homotopy, finite-dimensional cohomology, and positive Euler characteristic.Making use of Whitehead's certain exact sequence, this paper aims to study the group ℰ(X) of self-homotopy equivalences of X and its subgroup ℰ * (X) constituted by elements inducing the identity on the homology groups.Specifically, we prove that ℰ * (X) is trivial and ℰ(X) is isomorphic to a certain subgroup of ℚ * × ℰ(X m-1 ), where m is the formal dimension of X, X m-1 is its (m -1)-skeleton, and ℚ * = ℚ\{0}.