Low Dimensional Topology via Differential Equations

[803166]这个项目将继续Mrowka对三维和四维流形（时空数学模型）的研究。这些研究集中在各种数学物理方程（主要是Yang-Mills方程和sieberg - wittenequation）的解和解的空间的性质与携带这些方程的时空拓扑的关系上。这一策略在过去的二十年中非常成功，正如Yau、Schoen、Taubes、Donaldson和uhlenbeck的工作所证明的那样。Mrowka希望在与Kronheimer的合作中解决一个关于三维空间拓扑结构的30年猜想，即性质P猜想，这是向spoincare的猜想迈出的重要一步，即封闭三维时空的最简单模型的特征是每个闭环都可以收缩到一个点而不离开时空

9803166Mrowka This project will continue Mrowka's investigations into the studyof three- and four-dimensional manifolds (mathematical models forspace-time). These investigations center on relating properties ofsolutions and spaces of solutions of the various equations ofmathematical physics (primarily the Yang-Mills and Sieberg-Wittenequations) to the topology of the space-times that carry theequations. This strategy has been very successful in the past twentyyears, as evidenced by work of Yau, Schoen, Taubes, Donaldson, andUhlenbeck. Mrowka hopes in joint work with Kronheimer to resolve a30-year-old conjecture about the topology of three-dimensional spacesknown as the Property P conjecture, an important step towardsPoincare's conjecture that the simplest model of a closedthree-dimensional space-time is characterized by the property thatevery closed loop is contractible to a point without leaving thespace-time.***