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, Volume 159, Issue 1–2, pp 161–170 | Cite as

Lie models for nilpotent spaces

  • Yves Félix
  • José M. Moreno-Fernández
  • Daniel TanréEmail author
Article
  • 20 Downloads

Abstract

Let (Ld) be a differential graded Lie algebra, where \(L={\mathbb {L}}(V)\) is free as graded Lie algebra and \(V=V_{\ge 0}\) is a finite type graded vector space. We prove that the injection of (Ld) into its completion \((\widehat{L},d)\) is a quasi-isomorphism if and only if H(Ld) 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.

Mathematics Subject Classification

Primary 55P62 Secondary 55P60 16W60 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yves Félix
    • 1
  • José M. Moreno-Fernández
    • 2
  • Daniel Tanré
    • 3
    Email author
  1. 1.Institut de Mathématiques et PhysiqueUniversité Catholique de Louvain-la-NeuveLouvain-la-NeuveBelgique
  2. 2.Departamento de Algebra, Geometría y TopologíaUniversidad de MálagaMálagaSpain
  3. 3.Département de Mathématiques, UMR 8524Université de Lille 1Villeneuve d’Ascq CedexFrance

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