# Are isospectral manifolds necessarily homeomorphic?

It's known that there are pairs of closed Riemannian manifolds which are isospectral but not isometric. Is it known if there are closed Riemannian manifolds which are isospectral but not homeomorphic? (By isospectral, I mean that the Laplace-Beltrami operator on functions has the same spectrum on both manifolds.)

Thanks,

Dmitri

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@Joel: For hyperbolic manifolds of dimension $>2$ homonorphism implies isometry (Mostow Rigidity). –  Misha Jan 2 '13 at 23:16