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A Proof of the Hilbert-Smith Conjecture

Louis F. McAuley
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Abstract

The Hilbert-Smith Conjecture states that if G is a locally compact group which acts effectively on a connected manifold as a topological transformation group, then G is a Lie group. A rather straightforward proof of this conjecture is given. The motivation is work of Cernavskii (``Finite-to-one mappings of manifolds'', Trans. of Math. Sk. 65 (107), 1964.) His work is generalized to the orbit map of an effective action of a p-adic group on compact connected n-manifolds with the aid of some new ideas. There is no attempt to use Smith Theory even though there may be similarities.

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Louis F. McAuley. 2001-12-07. A Proof of the Hilbert-Smith Conjecture. https://arxiv.org/abs/math/0103215

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