同调协群的无穷秩和

IF 2.3 1区数学 Q1 MATHEMATICS

Duke Mathematical Journal Pub Date : 2023-09-01 DOI:10.1215/00127094-2022-0082

Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong

{"title":"同调协群的无穷秩和","authors":"Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong","doi":"10.1215/00127094-2022-0082","DOIUrl":null,"url":null,"abstract":"We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains a Z∞-subgroup and a Z-summand. Our proof proceeds by introducing an algebraic variant of the involutive Heegaard Floer package of Hendricks, Manolescu, and Zemke. This is inspired by an analogous argument in the setting of knot concordance due to the second author.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"26","resultStr":"{\"title\":\"An infinite-rank summand of the homology cobordism group\",\"authors\":\"Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong\",\"doi\":\"10.1215/00127094-2022-0082\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains a Z∞-subgroup and a Z-summand. Our proof proceeds by introducing an algebraic variant of the involutive Heegaard Floer package of Hendricks, Manolescu, and Zemke. This is inspired by an analogous argument in the setting of knot concordance due to the second author.\",\"PeriodicalId\":11447,\"journal\":{\"name\":\"Duke Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"26\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Duke Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1215/00127094-2022-0082\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Duke Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1215/00127094-2022-0082","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 26

摘要

我们证明了三维同调配群允许一个无穷秩和。已知同调协群包含一个Z∞子群和一个Z-和。我们的证明通过引入Hendricks, Manolescu和Zemke的对合Heegaard flower包的代数变体来进行。这是启发了类似的论点，在结和谐的设置，由于第二作者。

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

An infinite-rank summand of the homology cobordism group

We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains a Z∞-subgroup and a Z-summand. Our proof proceeds by introducing an algebraic variant of the involutive Heegaard Floer package of Hendricks, Manolescu, and Zemke. This is inspired by an analogous argument in the setting of knot concordance due to the second author.

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

Duke Mathematical Journal 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Information not localized