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 . 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.
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