{"paper":{"title":"Strongly isospectral manifolds with nonisomorphic cohomology rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.DG","authors_text":"Emilio A. Lauret, Juan Pablo Rossetti, Roberto J. Miatello","submitted_at":"2011-03-01T18:51:58Z","abstract_excerpt":"For any $n\\geq 7$, $k\\geq 3$, 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 t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0249","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}