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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Transitive actions on highly connected spaces


Author: Victor Schneider
Journal: Proc. Amer. Math. Soc. 38 (1973), 179-185
MSC: Primary 57E15
DOI: https://doi.org/10.1090/S0002-9939-1973-0321125-9
MathSciNet review: 0321125
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Abstract: Let $ G$ be a compact, connected Lie group and $ H$ a closed subgroup of $ G$. It is shown that if $ G/H$ is highly connected relative to $ \operatorname{Rk} (G) - \operatorname{Rk} (H),G/H$ splits as a product of homogeneous spaces of simple Lie groups. This is used to show that the only transitive, effective actions on a large class of products of spheres are products of the known actions on the individual spheres.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0321125-9
Keywords: Transitive action, $ n$-connected, Lie group, Steenrod operations
Article copyright: © Copyright 1973 American Mathematical Society