The MilnorMoore theorem for $L_\infty$ algebras in rational homotopy theory
Abstract
We give a construction of the universal enveloping $A_\infty$ algebra of a given $L_\infty$ algebra, alternative to the already existing versions. As applications, we derive a higher homotopy algebras version of the classical MilnorMoore theorem, proposing a new $A_\infty$ model for simply connected rational homotopy types, and uncovering a relationship between the higher order rational Whitehead products in homotopy groups and the PontryaginMassey products in the rational loop space homology algebra.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 DOI:
 10.48550/arXiv.1904.12530
 arXiv:
 arXiv:1904.12530
 Bibcode:
 2019arXiv190412530M
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Representation Theory;
 55P62;
 16S30;
 17B55;
 18G55;
 16E45;
 55S30;
 55Q15