{"paper":{"title":"Fixed points of circle actions on spaces with rational cohomology of $S^n V S^{2n} V S^{3n}$ or $P^2(n) V S^{3n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mahender Singh","submitted_at":"2007-12-14T12:02:12Z","abstract_excerpt":"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 $X\\hookrightarrow X_{\\mathbb{S}^1} \\longrightarrow B_{\\mathbb{S}^1}$. We also give examples realizing the possible cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.2329","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}