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arXiv · 1706.09194

Lie models for nilpotent spaces

Yves Félix·José Moreno-Fernández·Daniel Tanré
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Abstract

Let $(L,d)$ be a differential graded Lie algebra, where $L=L(V)$ is free as graded Lie algebra and $V=V_{\geq 0}$ is a finite type graded vector space. We prove that the injection of $(L,d)$ into its completion $(\widehat{L},d)$ is a quasi-isomorphism if and only if $H(L,d)$ is a finite type pronilpotent graded Lie algebra. As a consequence, we obtain an equivalence between graded Lie models for nilpotent spaces in rational homotopy theory.

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BibTeXRIS

Yves Félix, José Moreno-Fernández, Daniel Tanré. 2017-06-28. Lie models for nilpotent spaces. https://doi.org/10.1007/s00229-018-1038-8

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