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

我在几何和拓扑学领域工作。更确切地说，我正在研究纽结理论；这是一个拓扑学、几何学和代数几何相互作用的领域。在我的项目中，我感兴趣的是找出L-空间纽结的分支覆盖是否(以及在什么条件下)是L-空间，并更一般地回答关于这些空间的L-空间猜想。我正在使用汉塞尔曼-拉斯穆森-沃森的边界弗洛尔理论来回答这些问题。此外，我正在考虑建立上述弗洛尔理论和规范理论之间的联系，如Seiberg-Witten理论或瞬子Floer理论。

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.