与有边界曲面相关的同调代数

IF 1 2区数学 Q1 MATHEMATICS Quantum Topology Pub Date : 2015-08-11 DOI:10.4171/qt/144

K. Cieliebak, K. Fukaya, J. Latschev

{"title":"与有边界曲面相关的同调代数","authors":"K. Cieliebak, K. Fukaya, J. Latschev","doi":"10.4171/qt/144","DOIUrl":null,"url":null,"abstract":"In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic structure for all three contexts is a homotopy version of involutive bi-Lie algebras, which we call IBL$_\\infty$-algebras.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"2016 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2015-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"36","resultStr":"{\"title\":\"Homological algebra related to surfaces with boundary\",\"authors\":\"K. Cieliebak, K. Fukaya, J. Latschev\",\"doi\":\"10.4171/qt/144\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic structure for all three contexts is a homotopy version of involutive bi-Lie algebras, which we call IBL$_\\\\infty$-algebras.\",\"PeriodicalId\":51331,\"journal\":{\"name\":\"Quantum Topology\",\"volume\":\"2016 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2015-08-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"36\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/qt/144\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/qt/144","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 36

摘要

在本文中，我们描述了一个代数框架，它可以在三个相关但不同的背景下使用:弦拓扑，辛场论和拉格朗日高属花理论。结果表明，这三种情况下的相关代数结构是对合双李代数的同伦版本，我们称之为IBL $_\infty$ -代数。

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

本刊更多论文

Homological algebra related to surfaces with boundary

In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic structure for all three contexts is a homotopy version of involutive bi-Lie algebras, which we call IBL$_\infty$-algebras.

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

来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.