{"title":"全纯盘和纤维拉格朗日的盘势","authors":"Douglas Schultz","doi":"10.4310/JSG.2021.v19.n1.a4","DOIUrl":null,"url":null,"abstract":"We consider a fibered Lagrangian $L$ in a compact symplectic fibration with small monotone fibers, and develop a strategy for lifting $J$-holomorphic disks with Lagrangian boundary from the base to the total space. In case $L$ is a product, we use this machinery to give a formula for the leading order potential and formulate an unobstructedness criteria for the $A_\\infty$ algebra. We provide some explicit computations, one of which involves finding an embedded 2n+k dimensional submanifold of Floer-non-trivial tori in an 2n+2k dimensional fiber bundle.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"150 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Holomorphic disks and the disk potential for a fibered Lagrangian\",\"authors\":\"Douglas Schultz\",\"doi\":\"10.4310/JSG.2021.v19.n1.a4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a fibered Lagrangian $L$ in a compact symplectic fibration with small monotone fibers, and develop a strategy for lifting $J$-holomorphic disks with Lagrangian boundary from the base to the total space. In case $L$ is a product, we use this machinery to give a formula for the leading order potential and formulate an unobstructedness criteria for the $A_\\\\infty$ algebra. We provide some explicit computations, one of which involves finding an embedded 2n+k dimensional submanifold of Floer-non-trivial tori in an 2n+2k dimensional fiber bundle.\",\"PeriodicalId\":50029,\"journal\":{\"name\":\"Journal of Symplectic Geometry\",\"volume\":\"150 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2018-04-11\",\"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.n1.a4\",\"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.n1.a4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Holomorphic disks and the disk potential for a fibered Lagrangian
We consider a fibered Lagrangian $L$ in a compact symplectic fibration with small monotone fibers, and develop a strategy for lifting $J$-holomorphic disks with Lagrangian boundary from the base to the total space. In case $L$ is a product, we use this machinery to give a formula for the leading order potential and formulate an unobstructedness criteria for the $A_\infty$ algebra. We provide some explicit computations, one of which involves finding an embedded 2n+k dimensional submanifold of Floer-non-trivial tori in an 2n+2k dimensional fiber bundle.
期刊介绍:
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.