Do the Hodge Spectra Distinguish Orbifolds from Manifolds? Part 1
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 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 ≤ 3. This is enough to distinguish orbifolds from manifolds for dimension ≤ 3.
571-598
Gittins, Katie
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Gordon, Carolyn
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Khalile, Magda
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Solis, Ingrid Membrillo
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Sandoval, Mary
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Stanhope, Elizabeth
13f41f89-11b7-4505-9f99-02fef2ca6497
July 2024
Gittins, Katie
fed30e0d-906f-4777-950d-0a4ab55fc5c3
Gordon, Carolyn
f977b47f-99e5-4908-bdc6-574e9c960b44
Khalile, Magda
5e9f29b6-848b-4f11-9681-32f8038a97bf
Solis, Ingrid Membrillo
c458faf5-8cdb-4618-ba90-f8a90209f20a
Sandoval, Mary
14bbc8a5-5851-4c5e-ba3b-d4ab618ab3d8
Stanhope, Elizabeth
13f41f89-11b7-4505-9f99-02fef2ca6497
Gittins, Katie, Gordon, Carolyn, Khalile, Magda, Solis, Ingrid Membrillo, Sandoval, Mary and Stanhope, Elizabeth
(2024)
Do the Hodge Spectra Distinguish Orbifolds from Manifolds? Part 1.
Michigan Mathematical Journal, 74 (3), .
(doi:10.1307/mmj/20216126).
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 ≤ 3. This is enough to distinguish orbifolds from manifolds for dimension ≤ 3.
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Accepted/In Press date: 15 November 2021
Published date: July 2024
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© 2024 University of Michigan. All rights reserved.
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Local EPrints ID: 492623
URI: http://eprints.soton.ac.uk/id/eprint/492623
ISSN: 0026-2285
PURE UUID: 2b66fd7c-04bb-4e04-a03f-bbe2548e767b
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Date deposited: 08 Aug 2024 16:34
Last modified: 19 Dec 2024 02:55
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Contributors
Author:
Katie Gittins
Author:
Carolyn Gordon
Author:
Magda Khalile
Author:
Mary Sandoval
Author:
Elizabeth Stanhope
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