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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
References
Publication
Received: 18 August 2014
Revised: 3 November 2014
Accepted: 25 November 2014
Published: 10 September 2015
Authors
Michael Levin
Department of Mathematics
Ben Gurion University of the Negev
PO Box 653
Be’er Sheva 84105
Israel