Detecting L-spaces among branched covers of L-space knots

检测 L 空间结的分支覆盖之间的 L 空间

• 批准号: 1950953
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1950953
• 关键词: Detecting; spaces; among; branched; covers

I am working in the area of geometry and topology. More precisely, I am working on knot theory; a field in interplay of topology, geometry and algebraic geometry. In my project I am interested in finding if (and under what conditions) a branched cover of an L-space knot is an L-space and, more generally, answering the L-space conjecture for these spaces. I am using bordered Floer theory of Hanselman-Rasmussen-Watson to answer these questions. Moreover, I am thinking about establishing relations between the said Floer theory and gauge theories like Seiberg-Witten theory or instanton Floer theory.

我在几何学和拓扑学领域工作。更确切地说，我正在研究纽结理论;拓扑学，几何学和代数几何学相互作用的领域。在我的项目中，我感兴趣的是寻找是否（以及在什么条件下）L-空间结的分支覆盖是L-空间，更一般地说，回答这些空间的L-空间猜想。我正在使用Hanselman-Rasmussen-沃森的有界Floer理论来回答这些问题。此外，我还在考虑建立上述弗洛尔理论与塞伯格-威滕理论或瞬子弗洛尔理论等规范理论之间的关系。