Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A counterexample to the HK-conjecture that is principal   Scarparo has constructed counterexamples to Matui's HK-conjecture. These
counterexample and other known counterexamples are essentially principal but
not principal. In the present paper, a counterexample to the HK-conjecture that
is principal is given. Like Scarparo's original counterexample, our
counterexample is the transformation groupoid associated to a particular
odometer. However, the relevant group is the fundamental group of a flat
manifold (and hence is torsion-free) and the associated odometer action is
free. The examples discussed here do satisfy the rational version of the
HK-conjecture.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: physics