Maurer-Cartan moduli and homotopy theory

Maurer-Cartan 模量和同伦理论

• 批准号: EP/I014012/1
• 负责人: Andrey Lazarev
• 金额: $ 3.09万
• 依托单位: University of Leicester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI014012%2F1
• 关键词: Maurer; Cartan; moduli; homotopy; theory

The area of the proposed research comprises those aspects of homological algebra and topology which use methods from other areas of mathematics such as algebraic and differential geometry as well as ideas and intuition from theoretical physics.The notions of a Maurer-Cartan element an Maurer-Cartan equation (also known in physics as a master equation) are classical and indeed, go back to the classical papers of Maurer and Cartan written over 100 years ago; this is a standard tool in differential geomtery. It has been noticed that the Maurer-Cartan structures appear in various branches of mathematics and theoretical physics, from characteristic classes of foliations to conformal field theory. This notion has been considered by many authors from different points of view but until now a general treatment has been lacking.The present proposal intends to lay the foundations for the theory of Maurer-Cartan elements and their moduli spaces from the standpoint of rational homotopy theory. The developed apparatus will be applied to deformation theory and graph homology.

拟议研究的领域包括同调代数和拓扑的那些方面，它们使用其他数学领域（例如代数和微分几何）的方法以及理论物理学的思想和直觉。 Maurer-Cartan 元素和 Maurer-Cartan 方程（在物理学中也称为主方程）的概念是经典的，实际上，可以追溯到 Maurer 和 Cartan 撰写的经典论文 100多年前；这是微分几何中的标准工具。人们注意到毛雷尔-嘉当结构出现在数学和理论物理学的各个分支中，从叶状结构的特征类别到共形场论。许多作者从不同的角度考虑了这个概念，但迄今为止还缺乏一般性的处理。本提议旨在从有理同伦理论的角度为Maurer-Cartan元素及其模空间理论奠定基础。所开发的装置将应用于变形理论和图同源性。

项目成果

Disconnected rational homotopy theory

断开有理同伦理论

• DOI: 10.1016/j.aim.2015.07.009
• 发表时间: 2015
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Lazarev A