Do the Hodge spectra distinguish orbifolds from manifolds? Part 1

Gittins, Katie; Gordon, Carolyn; Khalile, Magda; Membrillo Solis, Ingrid; Sandoval, Mary; Stanhope, Elizabeth

Abstract

We examine the relationship between the singular set of a compact Riemann- ian 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 suffcient 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.

Citation

Gittins, K., Gordon, C., Khalile, M., Membrillo Solis, I., Sandoval, M., & Stanhope, E. (2023). Do the Hodge spectra distinguish orbifolds from manifolds? Part 1. Michigan Mathematical Journal, https://doi.org/10.1307/mmj/20216126

• Journal Article Type: Article
• Acceptance Date: Nov 12, 2021
• Online Publication Date: Jul 7, 2023
• Publication Date: 2023
• Deposit Date: Jan 18, 2022
• Journal: Michigan Mathematical Journal
• Print ISSN: 0026-2285
• Electronic ISSN: 1945-2365
• Publisher: Department of Mathematics
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1307/mmj/20216126
• Public URL: https://durham-repository.worktribe.com/output/1216747
• Publisher URL: https://projecteuclid.org/journals/michigan-mathematical-journal