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Homogeneous spaces with vanishing Steenrod squaring operations


Author: Victor Schneider
Journal: Proc. Amer. Math. Soc. 50 (1975), 451-458
MSC: Primary 57E25; Secondary 57F15
DOI: https://doi.org/10.1090/S0002-9939-1975-0405470-6
MathSciNet review: 0405470
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Abstract: If $ G$ is a compact, connected Lie group, $ H$ is a closed subgroup of $ G$ and $ G/H$ has no nonzero Steenrod operations, then $ G/H$ splits as a product of homogeneous spaces of simple Lie groups (the factors of $ G$). This fact is used to classify transitive actions on spaces with vanishing Steenrod operations, namely product of certain Stiefel manifolds and spheres.

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DOI: https://doi.org/10.1090/S0002-9939-1975-0405470-6
Keywords: Homogeneous space, Steenrod operations, spectral sequence
Article copyright: © Copyright 1975 American Mathematical Society

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