2015/09/22 by Andrew Nicas, Nicas, Andrew, David I. Rosenthal +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Coding theory and cryptography #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Primary 20F69 #Secondary 20F65 #math.GT #math.MG #msc:20F65 #msc:20F69
paper · pdf · doi:10.48550/arxiv.1509.06437
The published version of this paper will appear in a volume of the London Mathematical Society Lecture Note Series as part of a conference proceedings dedicated to Ross Geoghegan on the occasion of his 70th birthday
arxiv created 2015/09/22 · openalex publication_date 2015/09/22 · arxiv updated 2015/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to provide some new tools to aid the study of decomposition complexity, a notion introduced by Guentner, Tessera and Yu. In this paper, three equivalent definitions for decomposition complexity are established. We prove that metric spaces with finite hyperbolic dimension have finite (weak) decomposition complexity, and we prove that the collection of metric families that are coarsely embeddable into Hilbert space is closed under decomposition. A method for showing that certain metric spaces do not have finite decomposition complexity is also discussed.