Open AccessGeodesic spaces of low Nagata dimension
Author(s) -
Martina Jørgensen,
Urs Lang
Publication year - 2021
Publication title -
annales fennici mathematici
Language(s) - English
Resource type - Journals
eISSN - 2737-114X
pISSN - 2737-0690
DOI - 10.54330/afm.112472
Subject(s) - injective function , mathematics , geodesic , pure mathematics , dimension (graph theory) , inductive dimension , metric space , hadamard transform , complex dimension , packing dimension , graph , dimension theory (algebra) , lipschitz continuity , mathematical analysis , topology (electrical circuits) , minkowski–bouligand dimension , combinatorics , fractal dimension , fractal
We show that every geodesic metric space admitting an injective continuous map into the plane as well as every planar graph has Nagata dimension at most two, hence asymptotic dimension at most two. This relies on and answers a question in a recent work by Fujiwara and Papasoglu. We conclude that all three-dimensional Hadamard manifolds have Nagata dimension three. As a consequence, all such manifolds are absolute Lipschitz retracts.