Parametrised gauge theory and positive scalar curvature

参数化规范理论和正标量曲率

• 批准号: DP170101054
• 负责人: Prof Mathai Varghese
• 金额: $ 21.95万
• 依托单位: The University of Adelaide
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-06-30 至 2020-06-29
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170101054
• 关键词: Parametrised; gauge; theory; positive; scalar

This project aims to study innovative extensions of Seiberg-Witten gauge theory with new applications to the topology of metrics of positive scalar curvature on four-dimensional manifolds. Since Atiyah-Bott, Donaldson, Hitchin, and Seiberg-Witten’s work on various equations in gauge theory, profound applications have changed the geometry and topology of low dimensional manifolds. Parametrised index theory has obtained deep results on the topology of metrics of positive scalar curvature in higher dimensions, but these methods do not work in the case of the fourth dimension. This project will develop (parametrised) Seiberg-Witten gauge theory as a new approach to the study of the topology of metrics of positive scalar curvature in four dimensions. Expected outcomes include new invariants related to positive scalar curvature in four dimensions.

本项目旨在研究Seiberg-Witten规范理论的创新扩展及其在四维流形上正标量曲率度量拓扑中的新应用。自从Atiyah-Bott， Donaldson， Hitchin和Seiberg-Witten在规范理论中对各种方程的研究以来，深刻的应用改变了低维流形的几何和拓扑结构。参数化指标理论已经在高维正标量曲率度量拓扑上得到了深入的结果，但这些方法不适用于四维情况。本项目将发展（参数化）Seiberg-Witten规范理论，作为研究四维正标量曲率度量拓扑的新方法。预期结果包括与四维正标量曲率相关的新不变量。