You can hear the local orientability of an orbifold

2019/10/08 by Richardson, Sean, Stanhope, Elizabeth
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 58J53 #Secondary 53C20

paper · doi:10.48550/arxiv.1910.03224

Abstract

A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold which is locally modeled on the quotient of a connected, open manifold under a finite group of isometries. If all of the isometries used to define the local structures of an entire orbifold are orientation preserving, we call the orbifold locally orientable. We use heat invariants to show that a Riemannian orbifold which is locally orientable cannot be Laplace isospectral to a Riemannian orbifold which is not locally orientable. As a corollary we observe that a Riemannian orbifold that is not locally orientable cannot be Laplace isospectral to a Riemannian manifold.

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