Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions

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dc.creatorLang, Urs
dc.creatorSchlichenmaier, Thilo
dc.date2004-10-04
dc.date.accessioned2026-07-07T05:12:49Z
dc.date.available2026-07-07T05:12:49Z
dc.descriptionWe discuss a variation of Gromov's notion of asymptotic dimension that was introduced and named Nagata dimension by Assouad. The Nagata dimension turns out to be a quasisymmetry invariant of metric spaces. The class of metric spaces with finite Nagata dimension includes in particular all doubling spaces, metric trees, euclidean buildings, and homogeneous or pinched negatively curved Hadamard manifolds. Among others, we prove a quasisymmetric embedding theorem for spaces with finite Nagata dimension in the spirit of theorems of Assouad and Dranishnikov, and we characterize absolute Lipschitz retracts of finite Nagata dimension.
dc.identifierhttps://arxiv.org/abs/math/0410048
dc.identifierhttp://arxiv.org/abs/math/0410048
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72724
dc.subjectMetric Geometry
dc.subjectGeometric Topology
dc.titleNagata dimension, quasisymmetric embeddings, and Lipschitz extensions
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