The homotopy fixed point sets of spheres actions on rational complexes (Q342969)

In this paper the authors describe the rational homotopy type of the homotopy fixed point sets of \(S^3\)-actions on rational spheres and rational complex projective spaces. They prove that in both cases the homotopy fixed point sets have the rational homotopy type of a product of rational spheres and rational complex projective spaces.NEWLINENEWLINEIn the second part of the paper they consider simply connected spaces \(M\) with \(\dim\pi_*(M)\otimes \mathbb Q<\infty\). Then the natural map \(M_{\mathbb Q}^{S^1}\to M_{\mathbb Q}^{hS^1}\) is a rational homotopy equivalence if and only if \(M\) is a product of \(\mathbb CP^\infty\).