On G-sets and Isospectrality

Abstract

We study finite G-sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: if M is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then M has isospectral non-isometric covers.

References in corpus (4)

• The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
• Linear Representations and Isospectrality with Boundary Conditions
• Laplace-isospectral hyperbolic 2-orbifolds are representation-equivalent
• Determining a semisimple group from its representation degrees