{"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":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"44 1","pages":""},"PeriodicalIF":0.6000,"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\":50029,\"journal\":{\"name\":\"Journal of Symplectic Geometry\",\"volume\":\"44 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2019-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Symplectic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/jsg.2021.v19.n4.a3\",\"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 Symplectic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jsg.2021.v19.n4.a3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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