Strongly isospectral manifolds with nonisomorphic cohomology rings

E.A .LAURET, ; R.J. MIATELLO; J.P.ROSSETTI

REVISTA MATEMATICA IBEROAMERICANA

UNIV AUTONOMA MADRID

Lugar: Madrid; Año: 2013 vol. 29 p. 611 - 634

0213-2230

For any $ngeq 7$, $kgeq 3$, we give pairs of compact flat $n$-manifolds $M, M´$ with holonomy groups $mathbb Z_2^k$, 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 K"ahler 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 K"ahler) having very different cohomology rings. In particular, the cardinalities of the sets of primitive forms are different for all manifolds.