# EQUIVARIANT PRINCIPAL BUNDLES OVER SPHERES AND COHOMOGENEITY ONE MANIFOLDS Academic Article

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### abstract

• We classify smooth ${\rm SO}(n)$-equivariant principal bundles over $S^n$ in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant $(\Pi, G)$-bundles over manifolds with cohomogeneity 1.2000 Mathematical Subject Classification: 55R91.

• January 2003