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Proceedings of the London Mathematical Society (1)

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$G$-STRUCTURES ON SPHERES
MARTIN ČADEK, MICHAEL CRABB
Journal:

Proceedings of the London Mathematical Society / Volume 93 / Issue 3 / November 2006

Published online by Cambridge University Press:

13 October 2006, pp. 791-816

Print publication:

November 2006
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A generalization of classical theorems on the existence of sections of real, complex and quaternionic Stiefel manifolds over spheres is proved. We obtain a complete list of Lie group homomorphisms $\rho : G \to G_n$, where $G_n$ is one of the groups $SO(n)$, $SU(n)$ or $Sp(n)$ and $G$ is one of the groups $SO(k)$, $SU(k)$ or $Sp(k)$, which reduce the structure group $G_n$ in the fibre bundle $G_n \to G_{n + 1} \to G_{n + 1} / G_n$.

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$G$-STRUCTURES ON SPHERES