The Hilbert-Smith conjecture for quasiconformal actions
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 66-70.

Voir la notice de l'article provenant de la source American Mathematical Society

This note announces a proof of the Hilbert–Smith conjecture in the quasiconformal case: A locally compact group $G$ of quasiconformal homeomorphisms acting effectively on a Riemannian manifold is a Lie group. The result established is true in somewhat more generality.
DOI : 10.1090/S1079-6762-99-00062-1

Martin, Gaven 1

1 Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
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Martin, Gaven. The Hilbert-Smith conjecture for quasiconformal actions. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 66-70. doi : 10.1090/S1079-6762-99-00062-1. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00062-1/

[1] Collar, A. R. On the reciprocation of certain matrices Proc. Roy. Soc. Edinburgh 1939 195 206

[2] Donaldson, S. K., Sullivan, D. P. Quasiconformal 4-manifolds Acta Math. 1989 181 252

[3] Iwaniec, Tadeusz, Martin, Gaven Quasiregular semigroups Ann. Acad. Sci. Fenn. Math. 1996 241 254

[4] Mayer, Volker Uniformly quasiregular mappings of Lattès type Conform. Geom. Dyn. 1997 104 111

[5] Maz’Ja, Vladimir G. Sobolev spaces 1985

[6] Maclane, Saunders Steinitz field towers for modular fields Trans. Amer. Math. Soc. 1939 23 45

[7] Raymond, Frank, Williams, R. F. Examples of 𝑝-adic transformation groups Ann. of Math. (2) 1963 92 106

[8] Repov , Du An, C̆Epin, Evgenij A proof of the Hilbert-Smith conjecture for actions by Lipschitz maps Math. Ann. 1997 361 364

[9] Rickman, Seppo Quasiregular mappings 1993

[10] Yang, Chung-Tao 𝑝-adic transformation groups Michigan Math. J. 1960 201 218

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