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A simple proof of Curtis’ connectivity theorem for Lie powers
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/hha.2020.v22.n2.a15
Sergei O. Ivanov 1 , Vladislav Romanovskii 1 , Andrei Semenov 2
Affiliation  

We give a simple proof of the Curtis' theorem: if $A_\bullet$ is $k$-connected free simplicial abelian group, then $L^n(A_\bullet)$ is an $k+ \lceil \log_2 n \rceil$-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.

中文翻译:

柯蒂斯关于李幂的连通性定理的简单证明

我们给出柯蒂斯定理的一个简单证明:如果 $A_\bullet$ 是 $k$-连通的自由单纯阿贝尔群,那么 $L^n(A_\bullet)$ 是一个 $k+ \lceil \log_2 n \rceil $-连接的单纯阿贝尔群,其中 $L^n$ 是 $n$-th Lie 幂的函子。在证明中,我们不使用柯蒂斯对李幂的分解。取而代之的是,我们使用 Chevalley-Eilenberg 复形作为自由李代数。
更新日期:2020-01-01
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