{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/strongly-isospectral-hyperbolic-3-manifolds","title":"Strongly isospectral hyperbolic 3-manifolds with nonisomorphic rational cohomology rings","arxiv_id":"2111.11454","date":"2021-11-22","proceeding":null,"authors":["Anda Tenie"],"abstract":"This paper shows that one cannot \"hear\" the rational cohomology ring of a hyperbolic 3-manifold. More precisely, while it is well-known that strongly isospectral manifolds have the same cohomology as vector spaces, we give an example of compact hyperbolic 3-manifolds that are strongly isospectral but have nonisomorphic rational cohomology rings. Along the way we implement a computer program which finds the nullity of the cup product map $H^1(M;\\mathbb{Q})\\wedge H^1(M;\\mathbb{Q})\\rightarrow H^2(M;\\mathbb{Q})$ for any aspherical space in terms of the presentation of the fundamental group.","url_abs":"https://arxiv.org/abs/2111.11454v1","url_pdf":"https://arxiv.org/pdf/2111.11454v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"strongly-isospectral-hyperbolic-3-manifolds","repo_url":"https://github.com/andatenie/cupaspherical","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}