Katie Gittins, Carolyn Gordon, Magda Khalile, I. M. Solis, Mary R. Sandoval, E. Stanhope
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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. We show that the heat invariants of the $0$-spectrum together with those of the $1$-spectrum for the corresponding Hodge Laplacians are sufficient to distinguish orbifolds with singularities from manifolds as long as the singular sets have codimension $\le 3.$ This is enough to distinguish orbifolds from manifolds for dimension $\le 3.$
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