Strength of convergence in the orbit space of a transformation group

2005/08/18 by Robert Archbold, Archbold, Robert, Astrid an Huef +1
Mathematics · #22D30 #46L05 #46L39 #57S05 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:22D30 #msc:46L05 #msc:46L39 #msc:57S05

paper · pdf · doi:10.48550/arxiv.math/0508342

27 pages

arxiv created 2005/08/18 · arxiv updated 2009/12/01

Abstract

Let (G, X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of quantifying the extent of non-properness of the action. These notions are linked via the representation theory of the transformation-group C*-algebra.

Related

• Strength of convergence in non-free transformation groups
• Strength of convergence in the orbit space of a groupoid
• Orbit Equivalence and Measured Group Theory
• A survey of Measured Group Theory
• Approximate equivalence of actions