For any , , we give pairs of compact flat -manifolds , with holonomy groups , that are strongly isospectral, hence isospectral on -forms for all values of , having nonisomorphic cohomology rings. Moreover, if is even, is Kähler while is not. Furthermore, with the help of a computer program we show the existence of large Sunada isospectral families; for instance, for and there is a family of eight compact flat manifolds (four of them Kähler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifolds.
Cite this article
Emilio A. Lauret, Roberto J. Miatello, Juan P. Rossetti, Strongly isospectral manifolds with nonisomorphic cohomology rings. Rev. Mat. Iberoam. 29 (2013), no. 2, pp. 611–634DOI 10.4171/RMI/732