On the nonexistence of slices for 𝑝-adic transformation groups

Franklin, Lawrence M.

doi:10.1090/S0002-9939-1971-0267039-2

On the nonexistence of slices for $p$-adic transformation groups
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by Lawrence M. Franklin PDF

Proc. Amer. Math. Soc. 27 (1971), 183-185 Request permission

Abstract:

If a compact Lie group acts effectively on a manifold, then local cross-sections to the orbit structure can be constructed. They are called slices. We prove that if a compact group acts effectively on a manifold, but it is not a Lie group, then a slice cannot exist at every point.

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