Geodesic
A simple proof of Curtis’ connectivity theorem for Lie powers
Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 251-258.

Voir la notice de l'article provenant de la source International Press of Boston

We give a simple proof of Curtis’ theorem: if $A_{\bullet}$ is a $k$-connected free simplicial abelian group, then $L^n (A_{\bullet})$ is a $k + \lceil \operatorname{log}_2 n \rceil$-connected simplicial abelian group, where $L^n$ is the $n$‑th Lie power functor. In the proof we do not use Curtis’ decomposition of Lie powers. Instead we use the Chevalley–Eilenberg complex for the free Lie algebra.
DOI : 10.4310/HHA.2020.v22.n2.a15
Keywords: homotopy theory, unstable Adams spectral sequence, simplicial group, connectivity, Chevalley–Eilenberg complex 
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Sergei O. Ivanov; Vladislav Romanovskii; Andrei Semenov. A simple proof of Curtis’ connectivity theorem for Lie powers. Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 251-258. doi : 10.4310/HHA.2020.v22.n2.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a15/

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