{"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"month":"07","doi":"10.48550/ARXIV.2507.11727","_id":"20580","oa":1,"department":[{"_id":"GradSch"},{"_id":"ChWo"}],"OA_place":"repository","date_updated":"2025-11-11T09:28:05Z","title":"Implicit representations of codimension-2 submanifolds and their prequantum structure","arxiv":1,"date_published":"2025-07-15T00:00:00Z","status":"public","article_processing_charge":"No","language":[{"iso":"eng"}],"type":"preprint","oa_version":"Preprint","year":"2025","citation":{"ama":"Chern A, Ishida S. Implicit representations of codimension-2 submanifolds and their prequantum structure. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">10.48550/ARXIV.2507.11727</a>","ista":"Chern A, Ishida S. Implicit representations of codimension-2 submanifolds and their prequantum structure. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">10.48550/ARXIV.2507.11727</a>.","apa":"Chern, A., &#38; Ishida, S. (n.d.). Implicit representations of codimension-2 submanifolds and their prequantum structure. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">https://doi.org/10.48550/ARXIV.2507.11727</a>","short":"A. Chern, S. Ishida, ArXiv (n.d.).","chicago":"Chern, Albert, and Sadashige Ishida. “Implicit Representations of Codimension-2 Submanifolds and Their Prequantum Structure.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">https://doi.org/10.48550/ARXIV.2507.11727</a>.","ieee":"A. Chern and S. Ishida, “Implicit representations of codimension-2 submanifolds and their prequantum structure,” <i>arXiv</i>. .","mla":"Chern, Albert, and Sadashige Ishida. “Implicit Representations of Codimension-2 Submanifolds and Their Prequantum Structure.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/ARXIV.2507.11727\">10.48550/ARXIV.2507.11727</a>."},"external_id":{"arxiv":["2507.11727"]},"corr_author":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2507.11727","open_access":"1"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"full_name":"Chern, Albert","last_name":"Chern","first_name":"Albert"},{"id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","first_name":"Sadashige","last_name":"Ishida","orcid":"0000-0002-3121-3100","full_name":"Ishida, Sadashige"}],"date_created":"2025-10-30T18:36:56Z","day":"15","publication_status":"draft","publication":"arXiv","abstract":[{"text":"This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. This reveals a prequantum bundle structure over the space of submanifolds, equipped with the well-known Marsden-Weinstein symplectic structure. This bundle allows a new physical interpretation of the Marsden-Weinstein structure as the curvature of a connection form, which measures the average of volumes swept by the deformation of the S^1-family of hypersurfaces, defined as the phases of a complex function implicitly representing a submanifold.","lang":"eng"}],"related_material":{"record":[{"status":"for_moderation","id":"20551","relation":"dissertation_contains"}]}}