Geodesic spaces of low Nagata dimension
Keywords:Asymptotic dimension, Assouad-Nagata dimension, planar graph, Hadamard manifold, absolute Lipschitz retract
AbstractWe 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.
How to Cite
Jørgensen, M., & Lang, U. (2021). Geodesic spaces of low Nagata dimension. Annales Fennici Mathematici, 47(1), 83–88. https://doi.org/10.54330/afm.112472
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