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A Sullivan rational space is a spaceXfor which the rationalization map \(\widetilde {\varphi }: X\to X_{\mathbb Q}\) is a homotopy equivalence. For instance, the rationalization of a finite type simply connected space is a Sullivan rational space. The main question is to know if this is the only example. We give partial answers to that problem and show how the cohomologies ofXand \(X_{\mathbb Q}\) can be very different in some situations.

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Sullivan Rational Spaces

  • 章节

  • 发表日期：

    2026年

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  • Yves Félix,
  • Steve Halperin

摘要

A Sullivan rational space is a spaceXfor which the rationalization map \(\widetilde {\varphi }: X\to X_{\mathbb Q}\) is a homotopy equivalence. For instance, the rationalization of a finite type simply connected space is a Sullivan rational space. The main question is to know if this is the only example. We give partial answers to that problem and show how the cohomologies ofXand \(X_{\mathbb Q}\) can be very different in some situations.