Author: Peter Bubenik
Title: Separated Lie models and the homotopy Lie algebra

Author's e-mail address: p.bubenik@csuohio.edu
AMS classification number: Primary 55P62; Secondary 17B55
arXiv submission number: math.AT/0406405
to appear in the Journal of Pure and Applied Algebra

Abstract:

 The homotopy Lie algebra of a simply connected topological space, X, is
given by the rational homotopy groups on the loop space of X. 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.  We give connections
to the radical of the homotopy Lie algebra and the Avramov-Felix
conjecture. Examples that are worked out in detail include wedges of
spheres on any "thickness" and connected sums of products of spheres.