使用$ECH = SWF$的拉格朗日环面不变量

Pub Date : 2019-10-08 DOI:10.4310/jsg.2021.v19.n4.a3

Chris Gerig

{"title":"使用$ECH = SWF$的拉格朗日环面不变量","authors":"Chris Gerig","doi":"10.4310/jsg.2021.v19.n4.a3","DOIUrl":null,"url":null,"abstract":"We construct distinguished elements in the embedded contact homology (and monopole Floer homology) of a 3-torus, associated with Lagrangian tori in symplectic 4-manifolds and their isotopy classes. They turn out not to be new invariants, instead they repackage the Gromov (and Seiberg-Witten) invariants of various torus surgeries. We then recover a result of Morgan-Mrowka-Szabo on product formulas for the Seiberg-Witten invariants along 3-tori.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lagrangian torus invariants using $ECH = SWF$\",\"authors\":\"Chris Gerig\",\"doi\":\"10.4310/jsg.2021.v19.n4.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct distinguished elements in the embedded contact homology (and monopole Floer homology) of a 3-torus, associated with Lagrangian tori in symplectic 4-manifolds and their isotopy classes. They turn out not to be new invariants, instead they repackage the Gromov (and Seiberg-Witten) invariants of various torus surgeries. We then recover a result of Morgan-Mrowka-Szabo on product formulas for the Seiberg-Witten invariants along 3-tori.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2019-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/jsg.2021.v19.n4.a3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jsg.2021.v19.n4.a3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们构造了与辛4流形及其同位素类中的拉格朗日环面相关的3环面的嵌入接触同调(和单极子花同调)中的区分元素。它们不是新的不变量，而是重新包装了各种环体手术的Gromov(和Seiberg-Witten)不变量。然后，我们恢复了沿3环面Seiberg-Witten不变量乘积公式的Morgan-Mrowka-Szabo结果。

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

微信好友朋友圈 QQ好友复制链接

Lagrangian torus invariants using $ECH = SWF$

We construct distinguished elements in the embedded contact homology (and monopole Floer homology) of a 3-torus, associated with Lagrangian tori in symplectic 4-manifolds and their isotopy classes. They turn out not to be new invariants, instead they repackage the Gromov (and Seiberg-Witten) invariants of various torus surgeries. We then recover a result of Morgan-Mrowka-Szabo on product formulas for the Seiberg-Witten invariants along 3-tori.

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