Research output: Contribution to journal › Article › peer-review

**A simple proof of curtis' connectivity theorem for lie powers.** / Ivanov, Sergei O.; Romanovskii, Vladislav; Semenov, Andrei.

Research output: Contribution to journal › Article › peer-review

Ivanov, SO, Romanovskii, V & Semenov, A 2020, 'A simple proof of curtis' connectivity theorem for lie powers', *Homology, Homotopy and Applications*, vol. 22, no. 2, pp. 251-258. https://doi.org/10.4310/HHA.2020.V22.N2.A15

Ivanov, S. O., Romanovskii, V., & Semenov, A. (2020). A simple proof of curtis' connectivity theorem for lie powers. *Homology, Homotopy and Applications*, *22*(2), 251-258. https://doi.org/10.4310/HHA.2020.V22.N2.A15

Ivanov SO, Romanovskii V, Semenov A. A simple proof of curtis' connectivity theorem for lie powers. Homology, Homotopy and Applications. 2020 May 6;22(2):251-258. https://doi.org/10.4310/HHA.2020.V22.N2.A15

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title = "A simple proof of curtis' connectivity theorem for lie powers",

abstract = "We give a simple proof of Curtis' theorem: if A• is a k-connected free simplicial abelian group, then Ln(A•) is a k + ⌈ log2 n⌉-connected simplicial abelian group, where Ln 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.",

keywords = "Chevalley eilenberg complex, Con-nectivity, Homotopy theory, Simplicial group, Unstable adams spectral sequence",

author = "Ivanov, {Sergei O.} and Vladislav Romanovskii and Andrei Semenov",

year = "2020",

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doi = "10.4310/HHA.2020.V22.N2.A15",

language = "English",

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journal = "Homology, Homotopy and Applications",

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AU - Ivanov, Sergei O.

AU - Romanovskii, Vladislav

AU - Semenov, Andrei

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N2 - We give a simple proof of Curtis' theorem: if A• is a k-connected free simplicial abelian group, then Ln(A•) is a k + ⌈ log2 n⌉-connected simplicial abelian group, where Ln 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.

AB - We give a simple proof of Curtis' theorem: if A• is a k-connected free simplicial abelian group, then Ln(A•) is a k + ⌈ log2 n⌉-connected simplicial abelian group, where Ln 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.

KW - Chevalley eilenberg complex

KW - Con-nectivity

KW - Homotopy theory

KW - Simplicial group

KW - Unstable adams spectral sequence

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JO - Homology, Homotopy and Applications

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