JournalsrmiVol. 29, No. 2pp. 611–634

Strongly isospectral manifolds with nonisomorphic cohomology rings

  • Emilio A. Lauret

    Universidad Nacional de Córdoba, Argentina
  • Roberto J. Miatello

    Universidad Nacional de Córdoba, Argentina
  • Juan P. Rossetti

    Universidad Nacional de Córdoba, Argentina
Strongly isospectral manifolds with nonisomorphic cohomology rings cover

Abstract

For any n7n\ge 7, k3k\ge 3, we give pairs of compact flat nn-manifolds MM, MM' with holonomy groups Z2k\mathbb{Z}_2^k, that are strongly isospectral, hence isospectral on pp-forms for all values of pp, having nonisomorphic cohomology rings. Moreover, if nn is even, MM is Kähler while MM' is not. Furthermore, with the help of a computer program we show the existence of large Sunada isospectral families; for instance, for n=24n= 24 and k=3k=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.

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. 611–634

DOI 10.4171/RMI/732