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

In: Homology, Homotopy and Applications, Vol. 22, No. 2, 06.05.2020, p. 251-258.

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

Harvard

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

APA

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

Vancouver

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

Author

Ivanov, Sergei O. ; Romanovskii, Vladislav ; Semenov, Andrei. / A simple proof of curtis' connectivity theorem for lie powers. In: Homology, Homotopy and Applications. 2020 ; Vol. 22, No. 2. pp. 251-258.

BibTeX

@article{280b567ef0454aecb01b88bc765fa0c3,
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",
month = may,
day = "6",
doi = "10.4310/HHA.2020.V22.N2.A15",
language = "English",
volume = "22",
pages = "251--258",
journal = "Homology, Homotopy and Applications",
issn = "1532-0073",
publisher = "International Press of Boston, Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - A simple proof of curtis' connectivity theorem for lie powers

AU - Ivanov, Sergei O.

AU - Romanovskii, Vladislav

AU - Semenov, Andrei

PY - 2020/5/6

Y1 - 2020/5/6

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

UR - http://www.scopus.com/inward/record.url?scp=85086245494&partnerID=8YFLogxK

U2 - 10.4310/HHA.2020.V22.N2.A15

DO - 10.4310/HHA.2020.V22.N2.A15

M3 - Article

AN - SCOPUS:85086245494

VL - 22

SP - 251

EP - 258

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

SN - 1532-0073

IS - 2

ER -

ID: 62108094