Interactions between topology and geometry in low dimensions

这个博士项目将深入研究低维拓扑领域。在三维流形的领域中，拓扑结构和几何结构是相互联系的。这些相互作用在4维中不太强，但在研究3-流形作为4-流形的边界时变得突出。学生将探索拓扑和接触和辛几何之间的连接使用工具，如处理分解，柯比演算，德恩手术和莱夫谢茨纤维化。

This PhD project will delve into the area of low dimensional topology. In the realm of 3-manifolds the topological and the geometric structures inform each other. These interactions are less strong in dimension 4, but gain prominence when studying 3-manifolds as boundaries of 4-manifolds. The student will explore the connections between topology and contact and symplectic geometry using tools such as handle decompositions, Kirby calculus, Dehn surgeries and Lefschetz fibrations.