Title: Using heat invariants to study the Laplace spectral
geometry of orbifolds
Abstract: A Riemann orbifold is a mildly singular
generalization of a Riemannian manifold. In this talk we examine the
spectrum of the Laplace operator on functions, and more generally
that of the Hodge Laplacian on p-forms, in order to learn about the
topological structure of an orbifold. Our main tool is the list of
heat invariants associated to the p-spectrum of the corresponding
Hodge Laplacian. From the heat invariants of the 0-spectrum we
detect the local orientability of an orbifold in any dimension. The
heat invariants of the 0-spectrum together with those of the
1-spectrum are sufficient to distinguish singular orbifolds from
manifolds for dimension at most three.