Global and local boundedness of Polish groups

2012/03/27 by Rosendal, Christian
#46B04 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Primary: 22A25 #Secondary: 03E15

paper · doi:10.48550/arxiv.1203.6047

Abstract

We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on separable metric spaces). In particular, these properties are characterised by the orbit structure of isometric actions on metric spaces and isometric or continuous affine representations on separable Banach spaces.

Related

• On Roeckle-precompact Polish group which cannot act transitively on a complete metric space
• Locally Roelcke precompact Polish groups
• Polish globalization of Polish group partial actions
• Property (T) for Roelcke precompact Polish groups (after Ibarlucía, building on work of Ben Yaacov and Tsankov)
• Group actions on Polish spaces