Wreath products with the integers, proper actions and Hilbert space compression

2006/03/20 by Yves Stalder, Stalder, Yves, Alain Valette +1
Mathematics · #20E08 #20E22 #20F65 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #math.GR #msc:20E08 #msc:20E22 #msc:20F65

paper · pdf · doi:10.48550/arxiv.math/0603479

Minor corrections

openalex publication_date 2006/03/20 · arxiv created 2006/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the properties of acting metrically properly on some space with walls or some CAT(0) cube complex are closed by taking the wreath product with \Z. We also give a lower bound for the (equivariant) Hilbert space compression of H\wr\Z in terms of the (equivariant) Hilbert space compression of H.

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