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Do the Hodge spectra distinguish orbifolds from manifolds? Part 1

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

Authors

Carolyn Gordon

Magda Khalile

Ingrid Membrillo Solis

Mary Sandoval

Elizabeth Stanhope



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
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