Resolving rational cohomological dimension via a Cantor group action

Levin, Michael

doi:10.2140/agt.2015.15.2427

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Resolving rational cohomological dimension via a Cantor group action

Michael Levin

Algebraic & Geometric Topology 15 (2015) 2427–2437

DOI: 10.2140/agt.2015.15.2427

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

Volume 15, issue 4 (2015)