Gauge Theory and the Topology of Smooth Four-Manifolds

[9704174] fehan本项目处于几何拓扑学与数学物理的交叉领域。具体来说，研究者建立了光滑四流形的Donaldson和Seiberg-Witten不变量之间的等价性。研究人员将使用Pidstrigach和Tyurin首先提出的方法，该方法基于非量子思想。用于实现Pidstrigach-Tyurin方法的工具包括Taubes的胶合图和非abel单极子。光滑四维空间近年来受到了极大的关注，因为它们在相对论中的应用以及最近的一个数学发现允许它们的粗分类。值得注意的是，瞬子和单极子是光滑四流形分类中的两个主要成分，它们最初都是由研究基本粒子的物理学家引入的。

9704174 Feehan The project lies in the interface of geometric topology and mathematical physics. Specifically, the investigator is to establish the equivalence between Donaldson and Seiberg-Witten invariants for smooth four-manifolds. The investigator is to use the approach first suggested by Pidstrigach and Tyurin, which is based on non-quantum ideas. The tools to be used for implementing the Pidstrigach-Tyurin approach include Taubes's gluing maps and nonabelian monopoles. Smooth four-dimensional spaces have received a great deal of attention in recent years due to their applications in relativity theory and due to a recent mathematical discovery allowing their coarse classification. It is notable that instantons and monopoles, two major ingredients in the classification of smooth four-manifolds, both were originally introduced by the physicists studying elementary particles.