CLASSIFYING SPACES FOR FREE ACTIONS, AND THE HILBERT-SMITH CONJECTURE

Abstract

It is shown that any free action of a zero-dimensional compact group on the -dimensional Menger compactum is -universal for free actions, and that the orbit space is -classifying. Nonexistence of equivariant mappings between and implies that the orbit space has infinite dimension, where is any compact ANR-space with free action of the group of -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.