与有边界曲面相关的同调代数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2015-08-11 DOI:10.4171/qt/144

K. Cieliebak, K. Fukaya, J. Latschev

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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。

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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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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