A Simple proof of Curtis' connectivity theorem for Lie powers

Abstract

We give a simple proof of the Curtis' theorem: if A • is k-connected free simplicial abelian group, then L n (A • ) is an k + ⌈log 2 n⌉-connected simplicial abelian group, where L n is the functor of n-th Lie power. In the proof we do not use Curtis' decomposition of Lie powers. Instead of this we use the Chevalley-Eilenberg complex for the free Lie algebra.