{"title":"Lagrangian Cobordisms in Liouville manifolds","authors":"Valentin Bosshard","doi":"10.1142/S1793525322500030","DOIUrl":null,"url":null,"abstract":"Floer theory for Lagrangian cobordisms was developed by Biran and Cornea in a series of papers [BC13, BC14, BC17] to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. This paper explains how to use the language of stops to study Lagrangian cobordisms in Liouville manifolds and the associated exact triangles in the derived wrapped Fukaya category. Furthermore, we compute the cobordism groups of non-compact Riemann surfaces of finite type.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/S1793525322500030","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
Floer theory for Lagrangian cobordisms was developed by Biran and Cornea in a series of papers [BC13, BC14, BC17] to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. This paper explains how to use the language of stops to study Lagrangian cobordisms in Liouville manifolds and the associated exact triangles in the derived wrapped Fukaya category. Furthermore, we compute the cobordism groups of non-compact Riemann surfaces of finite type.
期刊介绍：
This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.
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