Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $K(\pi,1)$-conjecture implies the center conjecture for Artin groups   In this note, we prove that the $K(\pi,1)$-conjecture for Artin groups
implies the center conjecture for Artin groups. Specifically, every Artin group
without a spherical factor that satisfies the $K(\pi,1)$-conjecture has a
trivial center.

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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci