Transitive actions on highly connected spaces

Schneider, Victor

doi:10.1090/S0002-9939-1973-0321125-9

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.

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