2004/06/30 by Peter Bubenik
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:17B55 #msc:55P62
paper · pdf · doi:10.1016/j.jpaa.2007.05.018
published as J. Pure and Appl. Algebra, 212 (2008), no.2, 401--410 · 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
arxiv created 2007/05/07 · openalex publication_date 2007/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A simply connected topological space X has homotopy Lie algebra π_*(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.