Abstract
A simple way to evaluate the ranks of homotopy groups π 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 inG. 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.
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Original Russian Text © A. N. Shchetinin, 2009, published in Matematicheskie Zametki, 2009, Vol. 86, No. 6, pp. 912–924.
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Shchetinin, A.N. Ranks of homotopy groups of homogeneous spaces. Math Notes 86, 850–860 (2009). https://doi.org/10.1134/S0001434609110273
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DOI: https://doi.org/10.1134/S0001434609110273