an:01262285
Zbl 0988.57021
Maleshich, Iozhe
The Hilbert-Smith conjecture for H??lder actions
EN
Russ. Math. Surv. 52, No. 2, 407-408 (1997); translation from Usp. Mat. Nauk 52, No. 2, 173-174 (1997).
00043521
1997
j
57S10 54H15 22C05
Introduction: The Hilbert-Smith conjecture asserts that every compact group effectively acting on a manifold is a Lie group. It is known that for the solution of this conjecture it is sufficient to prove that the group of \(p\)-adic numbers cannot act effectively on a manifold. It was shown in [\textit{D. Repov??} and \textit{E. Shchepin}, Math. Ann. 308, No. 2, 361-364 (1997; Zbl 0879.57025)] that the \(p\)-adic numbers cannot act on a manifold by Lipschitz homeomorphisms. In this note it is shown that the same is true for H??lder actions with a large H??lder index.
Zbl 0879.57025