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



Are isospectral manifolds necessarily homeomorphic?
There's an example due to Doyle and Rossetti ("Tetra and Didi, the cosmic spectral twins"; <http://arxiv.org/abs/math.DG/0407422>) of 3-manifolds that are isospectral but not even homeomorphic. I don't know if this was the first such example.


