几乎是复杂的流形，总比为3

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-08-13 DOI:10.1142/s1793525323500164

Jiahao Hu

{"title":"几乎是复杂的流形，总比为3","authors":"Jiahao Hu","doi":"10.1142/s1793525323500164","DOIUrl":null,"url":null,"abstract":"We show the minimal total Betti number of a closed almost complex manifold of dimension $2n\\ge 8$ is four, thus confirming a conjecture of Sullivan except for dimension $6$. Along the way, we prove the only simply connected closed complex manifold having total Betti number three is the complex projective plane.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Almost complex manifolds with total betti number three\",\"authors\":\"Jiahao Hu\",\"doi\":\"10.1142/s1793525323500164\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show the minimal total Betti number of a closed almost complex manifold of dimension $2n\\\\ge 8$ is four, thus confirming a conjecture of Sullivan except for dimension $6$. Along the way, we prove the only simply connected closed complex manifold having total Betti number three is the complex projective plane.\",\"PeriodicalId\":49151,\"journal\":{\"name\":\"Journal of Topology and Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-08-13\",\"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/s1793525323500164\",\"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/s1793525323500164","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

我们证明了维数$2n\ \ 8$的闭几乎复流形的最小总Betti数为4，从而证实了Sullivan的一个猜想，除了维数$6$之外。在此过程中，我们证明了唯一具有总Betti数为3的单连通封闭复流形是复射影平面。

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

Almost complex manifolds with total betti number three

We show the minimal total Betti number of a closed almost complex manifold of dimension $2n\ge 8$ is four, thus confirming a conjecture of Sullivan except for dimension $6$. Along the way, we prove the only simply connected closed complex manifold having total Betti number three is the complex projective plane.

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.