Geodesic
Geodesic spaces of low Nagata dimension
Martina Jørgensen1 ; Urs Lang1
1 ETH Zürich, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 83-88.

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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.
DOI : 10.54330/afm.112472
Keywords: Asymptotic dimension, Assouad-Nagata dimension, planar graph, Hadamard manifold, absolute Lipschitz retract

Martina Jørgensen 1 ; Urs Lang 1

1 ETH Zürich, Department of Mathematics 
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Martina Jørgensen; Urs Lang. Geodesic spaces of low Nagata dimension. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 83-88. doi : 10.54330/afm.112472. http://geodesic.mathdoc.fr/articles/10.54330/afm.112472/

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