Strongly isospectral manifolds with nonisomorphic cohomology rings

LAURET, EMILIO A.; MIATELLO, ROBERTO J.; ROSSETTI, JUAN P.

REVISTA MATEMATICA IBEROAMERICANA

UNIV AUTONOMA MADRID

Año: 2013 vol. 29 p. 611 - 634

0213-2230

For any n ≥ 7, k ≥ 3, we give pairs of compact flat n-manifolds M,M´ with holonomy groups Zk2 , 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 Kähler 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 Kähler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifolds. © European Mathematical Society.