A Proof of the Hilbert-Smith Conjecture
Geometric Topology
2007-05-23 v8
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.
Cite
@article{arxiv.math/0103215,
title = {A Proof of the Hilbert-Smith Conjecture},
author = {Louis F. McAuley},
journal= {arXiv preprint arXiv:math/0103215},
year = {2007}
}
Comments
A few minors changes have been made on pages 6, 8, 19-20, 26, 28, 34 to make the paper easier to read