{"title":"增强型汉策定理","authors":"Michael H. Freedman","doi":"arxiv-2409.09983","DOIUrl":null,"url":null,"abstract":"A closed 3-manifold $M$ may be described up to some indeterminacy by a\nHeegaard diagram $\\mathcal{D}$. The question \"Does $M$ smoothly embed in\n$\\mathbb{R}^4$?'' is equivalent to a property of $\\mathcal{D}$ which we call\n$\\textit{doubly unlinked}$ (DU). This perspective leads to an enhancement of\nHantzsche's embedding obstruction.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Enhanced Hantzsche Theorem\",\"authors\":\"Michael H. Freedman\",\"doi\":\"arxiv-2409.09983\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A closed 3-manifold $M$ may be described up to some indeterminacy by a\\nHeegaard diagram $\\\\mathcal{D}$. The question \\\"Does $M$ smoothly embed in\\n$\\\\mathbb{R}^4$?'' is equivalent to a property of $\\\\mathcal{D}$ which we call\\n$\\\\textit{doubly unlinked}$ (DU). This perspective leads to an enhancement of\\nHantzsche's embedding obstruction.\",\"PeriodicalId\":501271,\"journal\":{\"name\":\"arXiv - MATH - Geometric Topology\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09983\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09983","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A closed 3-manifold $M$ may be described up to some indeterminacy by a
Heegaard diagram $\mathcal{D}$. The question "Does $M$ smoothly embed in
$\mathbb{R}^4$?'' is equivalent to a property of $\mathcal{D}$ which we call
$\textit{doubly unlinked}$ (DU). This perspective leads to an enhancement of
Hantzsche's embedding obstruction.
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