Geodesic
Classifying spaces for free actions, and the Hilbert–Smith conjecture
Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 137-144 
S. M. Ageev. Classifying spaces for free actions, and the Hilbert–Smith conjecture. Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 137-144. http://geodesic.mathdoc.fr/item/SM_1993_75_1_a7/
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     author = {S. M. Ageev},
     title = {Classifying spaces for free actions, and the {Hilbert{\textendash}Smith} conjecture},
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     volume = {75},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_75_1_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that any free action of a zero-dimensional compact group $G$ on the $n$-dimensional Menger compactum $M_n$ is $n$-universal for free actions, and that the orbit space $M_n/G$ is $n$-classifying. Nonexistence of equivariant mappings between $M_{n+m}$ and $M_n$ implies that the orbit space $R/A_p$ has infinite dimension, where $R$ is any compact ANR-space with free action of the group $A_p$ of $p$-adic integers. Knowledge of such nonexistence would then permit proof of the Hilbert–Smith conjecture under the assumption of finite dimensionality for the orbit space.

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