You can hear the local orientability of an orbifold

@article{Richardson2020YouCH,
  title={You can hear the local orientability of an orbifold},
  author={S. Richardson and Elizabeth Stanhope},
  journal={Differential Geometry and its Applications},
  year={2020}
}
Do the Hodge spectra distinguish orbifolds from manifolds? Part 1
We examine the relationship between the singular set of a compact Riemannian orbifold and the spectrum of the Hodge Laplacian on p-forms by computing the heat invariants associated to the p-spectrum.
One can’t hear orientability of surfaces
The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann

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One cannot hear orbifold isotropy type
Abstract.We show that the isotropy types of the singularities of Riemannian orbifolds are not determined by the Laplace spectrum. Indeed, we construct arbitrarily large families of mutually
Asymptotic expansion of the heat kernel for orbifolds
We study the relationship between the geometry and the Laplace spectrum of a Riemannian orbifoldO via its heat kernel; as in the manifold case, the time-zero asymptotic expansion of the heat kernel
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ON A GENERALIZATION OF THE NOTION OF MANIFOLD BY
where H is the product of the lengths of all the hooks in [X]. This formula is of general interest, since it gives a simple interpretation for the quotient n!/fX. Note that expression (2.2) is the
ON A GENERALIZATION OF THE NOTION OF MANIFOLD.
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TLDR
It is remarked in conclusion that an operator approach to the reduction the skew diagram [X] [ ] is also available, and Feit's formula was devised accordingly.
On ne peut pas entendre l'orientabilité d'une surface
On montre qu'il existe des paires de surfaces plates, a bord, qui sont isospectrales pour le laplacien avec condition au bord de Neumann; l'une est orientable, l'autre ne l'est pas. Ces surfaces ne
Erratum to ''Asymptotic expansion of the heat kernel for orbifolds''
PROFESSIONAL EXPERIENCE Professor, Department of Mathematics, Appalachian State University, 2009–present. Faculty Affiliate, Gender, Women’s & Sexuality Studies, Appalachian State University,
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