Transitive actions on highly connected spaces
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- by Victor Schneider PDF
- Proc. Amer. Math. Soc. 38 (1973), 179-185 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- 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