A Simple proof of Curtis' connectivity theorem for Lie powers
| Autor: | Andrei Semenov, Vladislav Romanovskii, Sergei O. Ivanov |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Functor Homotopy 010102 general mathematics 01 natural sciences Mathematics::Algebraic Topology Mathematics (miscellaneous) Simple (abstract algebra) Mathematics::Category Theory FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Abelian group Free Lie algebra Mathematics |
| DOI: | 10.48550/arxiv.1912.03086 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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