Do the Hodge Spectra Distinguish Orbifolds from Manifolds? Part 1

Abstract

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 with 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 $\le 3$.