论文标题
关于狄拉克运营商和申请家庭的讲座
Lectures on families of Dirac operators and applications
论文作者
论文摘要
这些是在2022年ICTP暑期学校“几何和拓扑的边境”上教授的微型菜单的音符。目的是介绍狄拉克运营商的家庭，以及如何用于研究几何和拓扑之间的相互作用。特别是，我们讨论了针对扭曲的狄拉克运营商家族的索引定理，及其在正标曲率和三维温斯坦猜想的指标上的应用。
These are the notes for a minicourse taught at the 2022 ICTP summer school `Frontiers in Geometry and Topology'. The goal is to introduce families of Dirac operators and how they can be used to study interactions between geometry and topology. In particular, we discuss the index theorem for families of twisted Dirac operators, and its applications to metrics of positive scalar curvature and the three-dimensional Weinstein conjecture.
