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Separated Lie Models And The Homotopy Lie Algebra, Peter G. Bubenik
Separated Lie Models And The Homotopy Lie Algebra, Peter G. Bubenik
Mathematics and Statistics Faculty Publications
Abstract. A simply connected topological space X has homotopy Lie algebra π∗(ΩX) ⊗ 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. 1.