The Hilbert-Smith Conjecture
| dc.creator | McAuley, Louis F. | |
| dc.date | 2001-03-23 | |
| dc.date | 2001-12-07 | |
| dc.date.accessioned | 2026-07-07T04:40:44Z | |
| dc.date.available | 2026-07-07T04:40:44Z | |
| dc.description | 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. It is well known that if a locally compact group acts effectively on a connected n-manifold M and G is not a Lie group, then there is a subgroup H of G isomorphic to a p-adic group A_p which acts effectively on M. It can be shown that A_p can not act effectively on an n-manifold and, hence, The Hilbert Smith Conjecture is true. The existence of a non empty fixed point set adds some complexity to the proof. In this paper, it is shown that A_p can not act freely on a compact connected n-manifold. The basic ideas for the general case are more clearly seen in this case. The general proof will be given in another paper. | |
| dc.description | A few minor changes have been made on pp. 6-8, 16-17, 22, 24 and 28 to make the paper easier to read | |
| dc.identifier | https://arxiv.org/abs/math/0103145 | |
| dc.identifier | http://arxiv.org/abs/math/0103145 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61124 | |
| dc.subject | Geometric Topology | |
| dc.title | The Hilbert-Smith Conjecture | |
| dc.type | text |