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arxiv: 0712.2329 · v4 · pith:ERBGPQHInew · submitted 2007-12-14 · 🧮 math.AT

Fixed points of circle actions on spaces with rational cohomology of S^n V S^(2n) V S^(3n) or P²(n) V S^(3n)

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keywords mathbbcohomologyrationalactionsfixedpossibleborelcases
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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.

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