3 copy edit

# Status of Hilbert-Smith conjecture and H-S conjecture for HolderHölder actions.

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 is $G$ a Lie group.

It was established for action actions by diffeomorphisms by Bochner and Montgomery. Later on it was also established for (compact?) actions by Lipschitz homeomorphisms (Repovs and Shchepin) and Holder action Hölder actions with very large exponent (>dim M/ dim M+2).

I am interested if the conjecture holds for Holder Hölder actions (with small exponents). Is it plausible these arguments can be pushed to get the conjecture for Holder Hölder actions? Or there is a fundamental obstruction?

Also, there is a 2001 preprint "A Proof of the Hilbert-Smith Conjecture" on arxiv that claims the full conjecture. I assume it's wrong as it wasn't published, but a comment from an expert would be highly appreciated.

2 retag and typo

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 is $G$ a Lie group.

It was established for action by diffeomorphisms by Bochner and Montgomery. Later on it was also established for (compact?) actions by Lipschitz homeomorphisms (Repovs and Shchepin) and Holder action with very large exponent (>dim M/ dim M+2).

I am interested if the conjecture holds for Holder actions (with small exponents). Is it plausible these arguments can be pushed to get the conjecture for Holder actions? Or there is a fundamental obstruction?

Also, there is a 2001 preprint "A Proof of the Hilbert-Smith Conjecture" on arxiv that claims the full conjecture. I assume it's wrong as it wasn't published, but a comment from an expert would be highly appreciated.

1

# Status of Hilbert-Smith conjecture and H-S conjecture for Holder actions.

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 is $G$ a Lie group.

It was established for action by diffeomorphisms by Bochner and Montgomery. Later on it was also established for (compact?) actions by Lipschitz homeomorphisms (Repovs and Shchepin) and Holder action with very large exponent (>dim M/ dim M+2).

I am interested if the conjecture holds for Holder actions (with small exponents). Is it plausible these arguments can be pushed to get the conjecture for Holder actions? Or there is a fundamental obstruction?

Also, there is a 2001 preprint "A Proof of the Hilbert-Smith Conjecture" on arxiv that claims the full conjecture. I assume it's wrong as it wasn't published, but a comment from an expert would highly appreciated.