Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of tiling $C^*$-algebras   We prove that Kellendonk's $C^*$-algebra of an aperiodic and repetitive
tiling with finite local complexity is classifiable by the Elliott invariant.
Our result follows from showing that tiling $C^*$-algebras are
$\mathcal{Z}$-stable, and hence have finite nuclear dimension. To prove
$\mathcal{Z}$-stability, we extend Matui's notion of almost finiteness to the
setting of \'etale groupoid actions following the footsteps of Kerr. To use
some of Kerr's techniques we have developed a version of the Ornstein-Weiss
quasitiling theorem for general \'etale groupoids.

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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th