Do the Hodge spectra distinguish orbifolds from manifolds? Part 1

2021/06/15 by Katie Gittins, Gittins, Katie, Carolyn S. Gordon +9 · 1 citation
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary: 58J53 #Secondary: 53C20 58J50 58J37

paper · pdf · doi:10.48550/arxiv.2106.07882

openalex publication_date 2021/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 ≤ 3. This is enough to distinguish orbifolds from manifolds for dimension ≤ 3.

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