The homotopy Lie algebra and the holonomy representation

  • Yves Félix
  • Stephen Halperin
  • Jean-Claude Thomas
Part of the Graduate Texts in Mathematics book series (GTM, volume 205)


In this section the ground ring is an arbitrary field k of characteristic zero. Recall from §21(d) that the homotopy Lie algebra, L x- of a simply connected topological space X is the graded vector space, equipped with a Lie bracket defined via the Whitehead product in π*(X). In particular, (cf. Example 2, §21) each xL x determines the linear transformation adx :L xL x, given by


Spectral Sequence Finite Type Infinite Sequence Affine Space Rational Homology 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Yves Félix
    • 1
  • Stephen Halperin
    • 2
  • Jean-Claude Thomas
    • 3
  1. 1.Institut MathematiquesUniversite de Louvain La NeuveLouvain-la-NeuveBelgium
  2. 2.College of Computer, Mathematical, and Physical ScienceUniversity of MarylandCollege ParkUSA
  3. 3.Faculte des SciencesUniversite d’AngersAngersFrance

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