Realizability of the group of rational self-homotopy equivalences

Abstract

For a 1-connected CW-complex $X$, let $\mathcal{E}(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$. The aim of this paper is to prove that, for every $n\in \mathbb{N}$, there exists a 1-connected rational CW-complex $X_n$ such that $\mathcal{E}(X_n)\cong \underset{2^{n+1}.times}{\underbrace{{\mathbb{Z}}_2\oplus ...\oplus {\mathbb{Z}}_2}}$.

References in corpus (1)

• Rational self-homotopy equivalences and Whitehead exact sequence

Cited by in corpus (5)

• Every finite group is the group of self homotopy equivalences of an elliptic space
• On the quasi-isomorphism type of a perfect chain algebra
• Adams-Hilton model and the group of self-homotopy equivalences of a simply connected cw-complex
• Certain maps preserving self-homotopy equivalences
• The effect of cell-attachment on the group of self-equivalences of an R-localized space