Inverse spectral geometry of toroidal warped products Annette Simonsen Abstract: In this paper we study a class of compact manifolds for which it is possible to determine the geometry if one knows the spectrum of the Laplace operator acting on functions at the manifold. We prove that two toroidal warped products are isometric if they have the same spectrum and satisfy some symmetry conditions. At the end of the paper we use scattering theory to obtain a similar result for non-compact manifolds. Keywords: Inverse spectral geometry, inverse scattering theory. MS classification: 58F19, 81U40.