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 -forms by computing the heat invariants associated to the -spectrum. We show that the heat invariants of the -spectrum together with those of the -spectrum for the corresponding Hodge Laplacians are sufficient to distinguish orbifolds with singularities from manifolds as long as the singular sets have codimension This is enough to distinguish orbifolds from manifolds for dimension
Cite
@article{arxiv.2106.07882,
title = {Do the Hodge spectra distinguish orbifolds from manifolds? Part 1},
author = {Katie Gittins and Carolyn Gordon and Magda Khalile and Ingrid Membrillo Solis and Mary Sandoval and Elizabeth Stanhope},
journal= {arXiv preprint arXiv:2106.07882},
year = {2021}
}
Comments
Part 2, joint with Juan Pablo Rossetti, will appear. V1 contained in addition to the results in Part 1 sections that examined information contained in the individual $p$-spectra. After realizing that Rossetti had overlapping results, we split the original paper into the current Part 1 together with a strengthened Part 2, joint with Rossetti, that combines our work on the individual $p$-spectra