Separated Lie models and the homotopy Lie algebra
arXiv:math/0406405 · doi:10.1016/j.jpaa.2007.05.018
Abstract
A simply connected topological space X has homotopy Lie algebra $Ï_*(ΩX) \tensor \Q$. 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.
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