The group of self-homotopy equivalences of a rational space cannot be a free abelian group

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<p>In this paper, we prove that a free abelian group cannot occur as the group of self-homotopy equivalences of a rational CW-complex of finite type. Thus, we generalize a result due to Sullivan–Wilkerson showing that if 𝑋 is a rational CW-complex of finite type such that dim 𝐻*(𝑋, ℤ) < ∞ or dim 𝜋*(𝑋) < ∞, then the group of self-homotopy equivalences of 𝑋 is isomorphic to a linear algebraic group defined over ℚ.</p>

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