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- W4288366318 abstract "Let $X$ be a connected space. An element $[f]in pi_n(X)$ is called rationally inert if $pi_*(X)otimes mathbb Q to pi_*(Xcup_fD^{n+1})otimes mathbb Q$ is surjective. We extend the results obtained in the simply connected case, and prove in particular that if $Xcup_fD^{n+1}$ is a Poincar'e duality complex and the algebra $H(X)$ requires at least two generators then $[f]in pi_n(X)$ is rationally inert. On the other hand, if $X$ is rationally a wedge of at least two spheres and $f$ is rationally non trivial, then $f$ is rationally inert. Finally if $f$ is rationally inert then the rational homotopy of the homotopy fibre of the injection $X to Xcup_fD^{n+1}$ is the completion of a free Lie algebra." @default.
- W4288366318 created "2022-07-29" @default.
- W4288366318 creator A5033627481 @default.
- W4288366318 creator A5067983610 @default.
- W4288366318 date "2019-04-18" @default.
- W4288366318 modified "2023-09-26" @default.
- W4288366318 title "Aspherical completions and rationally inert elements" @default.
- W4288366318 doi "https://doi.org/10.48550/arxiv.1904.08714" @default.
- W4288366318 hasPublicationYear "2019" @default.
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