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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)

Abstract

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

Keywords

Spectral Sequence Finite Type Infinite Sequence Affine Space Rational Homology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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