Fixed points of circle actions on spaces with rational cohomology of $S^{n}V{S}^{2n}V{S}^{3n}$ or $P^2(n)V{S}^{3n}$

Abstract

Let $X$ be a finitistic space with its rational cohomology isomorphic to that of the wedge sum $P^2(n)\vee S^{3n}$ or $S^n\vee S^{2n}\vee S^{3n}$. We study continuous ${\mathbb{S}}^1$ actions on $X$ and determine the possible fixed point sets up to rational cohomology depending on whether or not $X$ is totally non-homologous to zero in $X_{{\mathbb{S}}^1}$ in the Borel fibration $X\hookrightarrow X_{{\mathbb{S}}^1}⟶B_{{\mathbb{S}}^1}$. We also give examples realizing the possible cases.

arXiv comment10 pages, appeared in Archiv der Mathematik