Characterization of the Haagerup property for residually amenable groups

2016/05/16 by Orzechowski, Kamil
#20E26 #20F65 (primary) #51Fxx (secondary) #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1605.04830

Abstract

The notions of a box family and fibred cofinitely-coarse embedding are introduced. The countable, residually amenable groups satisfying the Haagerup property are then characterized as those possessing a box family that admits a fibred cofinitely-coarse embedding into a Hilbert space. This is a generalization of a result of X. Chen, Q. Wang and X. Wang on residually finite groups.

Related

• Coarse amenability at infinity
• Uniform Embeddability into Hilbert Space
• The Bounded Isomorphism Conjecture for Box Spaces of Residually Finite Groups
• Coarse embeddings at infinity and generalized expanders at infinity
• Residually finite amenable groups that are not Hilbert-Schmidt stable