Fixed points of circle actions on spaces with rational cohomology of Sn ÚS2n ÚS3n orP2(n) Ú S3nS^{n} vee S^{2n} vee S^{3n} {rm {bf or}}P^{2}(n) vee S^{3n}

摘要

Let X be a finitistic space with rational cohomology isomorphic to that of the wedge sum P2(n) ÚS3n or Sn ÚS2n ÚS3nP^{2}(n) vee S^{3n} {rm or} S^{n} vee S^{2n} vee S^{3n}. We study continuous mathbbS1{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_mathbbS1X_{{mathbb{S}}^{1}} in the Borel fibration $X hookrightarrow X_{{mathbb{S}}^{1}} rightarrown B_{{mathbb{S}}^{1}}$X hookrightarrow X_{{mathbb{S}}^{1}} rightarrown B_{{mathbb{S}}^{1}}. We also give examples realizing the possible cases.