Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak Modularity and $\widetilde{A}_n$ Buildings   The $\widetilde{A}_n$ Coxeter groups are known to not be systolic or
cocompactly cubulated for $n\geq 3$. We prove that these groups act
geometrically on weakly modular graphs, a weak notion of nonpositive curvature
generalizing the 1-skeleta of $\mathrm{CAT}(0)$ cube complexes and systolic
complexes. To prove weak modularity we describe the canonical emeddings of the
1-skeleta of $\widetilde{A}_n$ Coxeter complexes into the Euclidean spaces
$\mathbb{R}^{n+1}$. We also prove weak modularity for buildings of type
$\widetilde{A}_3$.

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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc