On actions of abelian Cantor groups

Michael Levin

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arXiv · 1910.00606

On actions of abelian Cantor groups

Michael Levin

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Abstract

By a Cantor group we mean a topological group homeomorphic to the Cantor set. The author earlier proved that every compact metric space of rational cohomological dimension n can be obtained as the orbit space of a Cantor group action on a metric compact space of covering dimension n. In this paper, we consider actions of abelian Cantor groups and, in particular, we show that in the result mentioned above the Cantor group can be assumed to be abelian for n>1.

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Michael Levin. 2019-10-01. On actions of abelian Cantor groups. https://arxiv.org/abs/1910.00606

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