Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal spectral triples on Kellendonk's $C^*$-algebra of a substitution
  tiling   We introduce a new class of noncommutative spectral triples on Kellendonk's
$C^*$-algebra associated with a nonperiodic substitution tiling. These spectral
triples are constructed from fractal trees on tilings, which define a geodesic
distance between any two tiles in the tiling. Since fractals typically have
infinite Euclidean length, the geodesic distance is defined using
Perron-Frobenius theory, and is self-similar with scaling factor given by the
Perron-Frobenius eigenvalue. We show that each spectral triple is
$\theta$-summable, and respects the hierarchy of the substitution system. To
elucidate our results, we construct a fractal tree on the Penrose tiling, and
explicitly show how it gives rise to a collection of spectral triples.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph