Volume 15, issue 4 (2015)

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Resolving rational cohomological dimension via a Cantor group action

Michael Levin

Algebraic & Geometric Topology 15 (2015) 2427–2437
Abstract

By a Cantor group we mean a topological group homeomorphic to the Cantor set. We show that a 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 $n$. Moreover, the action can be assumed to be free if $n=1$.

Keywords
cohomological dimension, transformation groups
Mathematical Subject Classification 2000
Primary: 55M10, 22C05
Secondary: 54F45