Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finiteness Properties of Certain Topological Graph Algebras   Let $E = (E^0, E^1, r, s)$ be a topological graph with no sinks such that
$E^0$ and $E^1$ are compact. We show that when $C^*(E)$ is finite, there is a
natural isomorphism $C^*(E) \cong C(E^\infty) \rtimes \mathbb{Z}$, where
$E^\infty$ is the infinite path space of $E$ and the action is given by the
backwards shift on $E^\infty$. Combining this with a result of Pimsner, we show
the properties of being AF-embeddable, quasidiagonal, stably finite, and finite
are equivalent for $C^*(E)$ and can be characterized by a natural
"combinatorial" condition on $E$.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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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: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph