This article is cited in 7 papers

Classifying spaces for free actions, and the Hilbert–Smith conjecture

S. M. Ageev

Brest State Pedagogical Institute

Abstract: 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.

MSC: Primary 57S10; Secondary 54C55, 54F45

Received: 19.07.1990

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1993, 75:1, 137–144

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