Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesic spaces of low Nagata dimension   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 very 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.

29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th