CONICET | Buscador de Institutos y Recursos Humanos

For any n>=7, k>=3, we give pairs of compact flat n-manifolds M, M´ with holonomy groups Z_2^k, that are strongly isospectral, hence isospectral on p-forms for all values of p, having nonisomorphic cohomology rings.Moreover, if n is even, M is Kaehler while M´ is not. Furthermore, with the help of a computer program we show the existence of large Sunada isospectral families; for instance, for n= 24 and k=3 there is a family of eight compact flat manifolds (four of them Kaehler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifolds.