Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sunada's method and the covering spectrum   In 2004, Sormani and Wei introduced the covering spectrum: a geometric
invariant that isolates part of the length spectrum of a Riemannian manifold.
In their paper they observed that certain Sunada isospectral manifolds share
the same covering spectrum, thus raising the question of whether the covering
spectrum is a spectral invariant. In the present paper we describe a group
theoretic condition under which Sunada's method gives manifolds with identical
covering spectra. When the group theoretic condition of our method is not met,
we are able to construct Sunada isospectral manifolds with distinct covering
spectra in dimension 3 and higher. Hence, the covering spectrum is not a
spectral invariant. The main geometric ingredient of the proof has an
interpretation as the minimum-marked-length-spectrum analogue of Colin de
Verdi\`{e}re's classical result on constructing metrics where the first $k$
eigenvalues of the Laplace spectrum have been prescribed.

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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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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: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc