Assuad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics

2008/04/29 by J. Higes, Higes, J.
Mathematics · #54C65 (Secondary) #54F45 (Primary) #55M10 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.0804.4533

openalex publication_date 2008/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose G is a countable, not necessarily finitely generated, group. We show G admits a proper, left-invariant metric d_G such that the Assouad-Nagata dimension of (G,d_G) is infinite, provided the center of G is not locally finite. As a corollary we solve two problems of A.Dranishnikov.

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