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Mat. Zametki, 2009, Volume 86, Issue 6, Pages 912–924 (Mi mz4891)  

This article is cited in 2 scientific papers (total in 2 papers)

Ranks of Homotopy Groups of Homogeneous Spaces

A. N. Shchetinin

N. E. Bauman Moscow State Technical University

Abstract: A simple way to evaluate the ranks of homotopy groups $\pi_j(M)$ is indicated for homogeneous spaces of the form $M=G/H$, where $G$ is a compact connected Lie group and $H$ is a connected regular subgroup or a subgroup of maximal rank in $G$. A classification of the spaces whose Onishchik ranks are equal to 3 is obtained. The transitive actions on the products of homogeneous spaces of the form $G/H$ are also described, where $G$ and $H$ are simple and $H$ is a subgroup of corank 1 in $G$ and the defect of the space $G/H$ is equal to 1.

Keywords: compact connected Lie group, homogeneous space, regular subgroup, homotopy group, rank of a group, Onishchik rank, Euler characteristic, semisimple group

DOI: https://doi.org/10.4213/mzm4891

Full text: PDF file (480 kB)
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English version:
Mathematical Notes, 2009, 86:6, 850–860

Bibliographic databases:

UDC: 512.816
Received: 20.03.2008
Revised: 23.01.2009

Citation: A. N. Shchetinin, “Ranks of Homotopy Groups of Homogeneous Spaces”, Mat. Zametki, 86:6 (2009), 912–924; Math. Notes, 86:6 (2009), 850–860

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. N. Shchetinin, “On factor-spaces of compact Lie groups by subgrops of co-rank one”, Russian Math. (Iz. VUZ), 59:6 (2015), 49–61  mathnet  crossref
    2. A. N. Shchetinin, “On coset-spaces of compact Lie groups by subgrops of corank two”, Russian Math. (Iz. VUZ), 61:11 (2017), 60–68  mathnet  crossref  isi
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