The panted cobordism groups of cusped hyperbolic 3-manifolds

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2022-07-12 DOI:10.1112/topo.12255

Hongbin Sun

{"title":"The panted cobordism groups of cusped hyperbolic 3-manifolds","authors":"Hongbin Sun","doi":"10.1112/topo.12255","DOIUrl":null,"url":null,"abstract":"<p>For any oriented cusped hyperbolic 3-manifold <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math>, we study its <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>R</mi>\n <mo>,</mo>\n <mi>ε</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(R,\\epsilon )$</annotation>\n </semantics></math>-panted cobordism group, which is the abelian group generated by <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>R</mi>\n <mo>,</mo>\n <mi>ε</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(R,\\epsilon )$</annotation>\n </semantics></math>-good curves in <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> modulo the oriented boundaries of <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>R</mi>\n <mo>,</mo>\n <mi>ε</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(R,\\epsilon )$</annotation>\n </semantics></math>-good pants. In particular, we prove that for sufficiently small <math>\n <semantics>\n <mrow>\n <mi>ε</mi>\n <mo>></mo>\n <mn>0</mn>\n </mrow>\n <annotation>$\\epsilon >0$</annotation>\n </semantics></math> and sufficiently large <math>\n <semantics>\n <mrow>\n <mi>R</mi>\n <mo>></mo>\n <mn>0</mn>\n </mrow>\n <annotation>$R>0$</annotation>\n </semantics></math>, some modified version of the <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>R</mi>\n <mo>,</mo>\n <mi>ε</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$(R,\\epsilon )$</annotation>\n </semantics></math>-panted cobordism group of <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> is isomorphic to <math>\n <semantics>\n <mrow>\n <msub>\n <mi>H</mi>\n <mn>1</mn>\n </msub>\n <mrow>\n <mo>(</mo>\n <mtext>SO</mtext>\n <mrow>\n <mo>(</mo>\n <mi>M</mi>\n <mo>)</mo>\n </mrow>\n <mo>;</mo>\n <mi>Z</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$H_1(\\text{SO}(M);\\mathbb {Z})$</annotation>\n </semantics></math>.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"15 3","pages":"1580-1634"},"PeriodicalIF":0.8000,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12255","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12255","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

Abstract

For any oriented cusped hyperbolic 3-manifold $M$ , we study its $(R, ε)$ -panted cobordism group, which is the abelian group generated by $(R, ε)$ -good curves in $M$ modulo the oriented boundaries of $(R, ε)$ -good pants. In particular, we prove that for sufficiently small $ε > 0$ and sufficiently large $R > 0$ , some modified version of the $(R, ε)$ -panted cobordism group of $M$ is isomorphic to $H_{1} (SO (M); Z)$ .

Abstract Image

查看原文本刊更多论文

顶角双曲3-流形的共轭群

对于任意有向双曲3流形M$ M$，我们研究了它的(R， ε)$ (R，\epsilon)$ -共轭群，它是由M$ M$中的(R， ε)$ (R，\epsilon)$ -good曲线模取(R)$的有向边界所生成的阿贝尔群，ε)$ (R，\epsilon)$ -好裤子。特别地，我们证明了当ε >0$ \ ε >0$和足够大的R >0$ R>0$，是(R)的修改版本，M$ M$的ε)$ (R，\ ε)$ -共轭群同构于h1 (SO (M);$H_1(\text{SO}(M);\mathbb {Z})$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.