{"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}
引用次数: 0
Abstract
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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