广义和球面3-流形的增强不变量界

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-03-23 DOI:10.1142/s1793525322500029

Geunho Lim

{"title":"广义和球面3-流形的增强不变量界","authors":"Geunho Lim","doi":"10.1142/s1793525322500029","DOIUrl":null,"url":null,"abstract":"We establish enhanced bounds on Cheeger–Gromov [Formula: see text]-invariants for general 3-manifolds and yet stronger bounds for special classes of 3-manifold. As key ingredients, we construct chain null-homotopies whose complexity is linearly bounded by its boundary. This result can be regarded as an algebraic topological analogue of Gromov’s conjecture for quantitative topology. The author hopes for applications to various fields including the smooth knot concordance group, quantitative topology and complexity theory.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"45 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Enhanced Bounds for rho-invariants for both general and spherical 3-manifolds\",\"authors\":\"Geunho Lim\",\"doi\":\"10.1142/s1793525322500029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish enhanced bounds on Cheeger–Gromov [Formula: see text]-invariants for general 3-manifolds and yet stronger bounds for special classes of 3-manifold. As key ingredients, we construct chain null-homotopies whose complexity is linearly bounded by its boundary. This result can be regarded as an algebraic topological analogue of Gromov’s conjecture for quantitative topology. The author hopes for applications to various fields including the smooth knot concordance group, quantitative topology and complexity theory.\",\"PeriodicalId\":49151,\"journal\":{\"name\":\"Journal of Topology and Analysis\",\"volume\":\"45 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-03-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Topology and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793525322500029\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793525322500029","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

我们建立了一般3-流形的Cheeger-Gromov[公式:见文本]不变量的增强界和特殊类型的3-流形的更强界。作为关键成分，我们构造了复杂度由其边界线性限定的链零同伦。这个结果可以看作是定量拓扑中Gromov猜想的代数拓扑类比。作者希望将其应用于光滑结协调群、定量拓扑和复杂性理论等各个领域。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Enhanced Bounds for rho-invariants for both general and spherical 3-manifolds

We establish enhanced bounds on Cheeger–Gromov [Formula: see text]-invariants for general 3-manifolds and yet stronger bounds for special classes of 3-manifold. As key ingredients, we construct chain null-homotopies whose complexity is linearly bounded by its boundary. This result can be regarded as an algebraic topological analogue of Gromov’s conjecture for quantitative topology. The author hopes for applications to various fields including the smooth knot concordance group, quantitative topology and complexity theory.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.