{"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/sasaki-einstein-7-manifolds-and-orlik-s","title":"Sasaki-Einstein 7-manifolds and Orlik's conjecture","arxiv_id":"2208.10666","date":"2022-08-23","proceeding":null,"authors":["Jaime Cuadros","Joe Lope"],"abstract":"We calculate the homology groups of certain 2-connected 7-manifolds admitting quasi-regular Sasaki-Einstein metrics. These manifolds are links that arise as Thom-Sebastiani sums of chain type singularities and cycle type singularities. Among these links, we found 52 new examples of Sasaki-Einstein rational homology 7-spheres and 124 new examples of Sasaki-Einstein 2-connected 7-manifolds homeomorphic to connected sums of $S^{3} \\times S^{4}.$ Furthermore, we found that manifolds of the form $k \\#\\left(S^{3} \\times S^{4}\\right)$ admit Sasaki-Einstein metrics for 22 different values of $k.$ We also describe the diffeomorphism type of certain families of homotopy 9-spheres admitting positive Ricci curvature. These manifolds are branched covers of $S^{11}$ branched over Sasaki-Einstein rational homology 7-spheres.","url_abs":"https://arxiv.org/abs/2208.10666v3","url_pdf":"https://arxiv.org/pdf/2208.10666v3.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":"sasaki-einstein-7-manifolds-and-orlik-s","repo_url":"https://github.com/jcuadrosvalle/codes-in-matlab","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"sasaki-einstein-7-manifolds-and-orlik-s","repo_url":"https://github.com/jcuadrosvalle/tables","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}