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

摘要

Let $X$ be a finitistic space with its rational cohomology isomorphic to thatof the wedge sum $P^2(n)ee S^{3n} $ or $S^{n} ee S^{2n}ee S^{3n}$. Westudy continuous $mathbb{S}^1$ actions on $X$ and determine the possible fixedpoint sets up to rational cohomology depending on whether or not $X$ is totallynon-homologous to zero in $X_{mathbb{S}^1}$ in the Borel fibration$Xhookrightarrow X_{mathbb{S}^1} longrightarrow B_{mathbb{S}^1}$. We alsogive examples realizing the possible cases.