Mathematical Sciences: Low-dimensional topology and geometry

数学科学：低维拓扑和几何

• 批准号: 9107505
• 负责人: Clinton McCrory
• 金额: $ 4.55万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107505&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Low; dimensional; topology

Matic will study a theory of moduli spaces of anti-self-dual connections for pairs, and a Yang-Mills theory for parabolic stable bundles in dimensions four and two. She will also work on Floer homology for rational homology spheres. This project also includes partial support for the annual Georgia Topology Conference. Matic's research combines theoretical physics with topology and differential geometry in the following way. The physics concerns topological quantum field theories. These lead to invariants of the underlying spaces on which they are defined. Although differential geometric constructions are involved as intermediaries, in the end quantities are derived which depend only on the topological and not the geometric character of the spaces.

马季奇将研究偶的反自对偶联络的模空间理论，以及四维和二维抛物稳定丛的Yang-Mills理论。她还将研究有理同调球面的Floer同调。该项目还包括对一年一度的佐治亚州拓扑学会议的部分支持。马季奇的研究通过以下方式将理论物理与拓扑学和微分几何相结合。物理学涉及到拓扑量子场理论。这些导致了定义它们的底层空间的不变量。虽然涉及到微分几何结构作为中介，但最终得到的量只取决于空间的拓扑性质，而不是几何特征。