On The Rational Realization of Even-dimensional Spheres and Products of Eilenberg--MacLane Spaces as Classifying Spaces

Yang Bai, Xiugui Liu, Jiaxi Zha

In this paper, we study the rational realization problem for the classifying space $B{\mathrm{aut}}_1(X)$. We prove that if $S^{2n}$ is realized as $B{\mathrm{aut}}_1(X{)}_{\mathbb{Q}}$…