Extension of Chekanov-Eliashberg algebra using annuli

Milica Dukic
{"title":"Extension of Chekanov-Eliashberg algebra using annuli","authors":"Milica Dukic","doi":"arxiv-2409.05856","DOIUrl":null,"url":null,"abstract":"We define an SFT-type invariant for Legendrian knots in the standard contact\n$\\mathbb{R}^3$. The invariant is a deformation of the Chekanov-Eliashberg\ndifferential graded algebra. The differential consists of a part that counts\nindex zero $J$-holomorphic disks with up to two positive punctures, annuli with\none positive puncture, and a string topological part. We describe the invariant\nand demonstrate its invariance combinatorially from the Lagrangian knot\nprojection, and compute some simple examples where the deformation is\nnon-vanishing.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Symplectic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05856","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

We define an SFT-type invariant for Legendrian knots in the standard contact $\mathbb{R}^3$. The invariant is a deformation of the Chekanov-Eliashberg differential graded algebra. The differential consists of a part that counts index zero $J$-holomorphic disks with up to two positive punctures, annuli with one positive puncture, and a string topological part. We describe the invariant and demonstrate its invariance combinatorially from the Lagrangian knot projection, and compute some simple examples where the deformation is non-vanishing.
利用环面扩展契卡诺夫-埃利亚什伯格代数
我们为标准接触$\mathbb{R}^3$中的传奇结定义了一个 SFT 型不变量。这个不变量是切卡诺夫-伊利亚斯伯格微分级数代数的变形。这个微分包括一个包含最多两个正穿刺的零$J$全形盘、一个包含正穿刺的环面和一个弦拓扑部分。我们描述了这个不变量,并从拉格朗日结投影的组合上证明了它的不变量性,还计算了一些变形不等的简单例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信