In topology a cell attachment \(f : S^n \to X\) is inert if the attachment does not create any new homotopy class, more precisely, if the induced map \(\pi _*(X)\to \pi _*(X\cup _fe^{n+1})\) is surjective. Here we consider the problem from the rational homotopy point of view and give criteria for \(\pi _*(X_{\mathbb Q})\to \pi _*((X\cup _fe^{n+1})_{\mathbb Q})\) to be surjective. Equivalent characterizations are given using minimal Sullivan models and profree dgl models.

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Inert Attachments

  • Yves Félix,
  • Steve Halperin

摘要

In topology a cell attachment \(f : S^n \to X\) is inert if the attachment does not create any new homotopy class, more precisely, if the induced map \(\pi _*(X)\to \pi _*(X\cup _fe^{n+1})\) is surjective. Here we consider the problem from the rational homotopy point of view and give criteria for \(\pi _*(X_{\mathbb Q})\to \pi _*((X\cup _fe^{n+1})_{\mathbb Q})\) to be surjective. Equivalent characterizations are given using minimal Sullivan models and profree dgl models.