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Separated Lie models and the homotopy Lie algebra

Peter Bubenik
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Abstract

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.

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Peter Bubenik. 2007-05-07. Separated Lie models and the homotopy Lie algebra. https://doi.org/10.1016/j.jpaa.2007.05.018

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