English

Separated Lie models and the homotopy Lie algebra

Algebraic Topology 2007-11-28 v3

Abstract

A simply connected topological space X has homotopy Lie algebra π(ΩX)\tensor\Q\pi_*(\Omega X) \tensor \Q. Following Quillen, there is a connected differential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of X, and whose homology is isomorphic to the homotopy Lie algebra. We show that such a Lie model can be replaced with one that has a special property we call separated. The homology of a separated dgL has a particular form which lends itself to calculations.

Keywords

Cite

@article{arxiv.math/0406405,
  title  = {Separated Lie models and the homotopy Lie algebra},
  author = {Peter Bubenik},
  journal= {arXiv preprint arXiv:math/0406405},
  year   = {2007}
}

Comments

Final version. To appear in the Journal of Pure and Applied Algebra. Added connections to the radical of the homotopy Lie algebra and the Avramov-Felix conjecture. Added examples of wedges of spheres of any "thickness" and connected sums of products of spheres. 15 pages

R2 v1 2026-07-22T17:06:56.853Z