标题： PU(2)单极子和四维流形不变量之间的关系 显示英文标题

标题： PU(2) monopoles and relations between four-manifold invariants

摘要： 利用量子场论的论证，威腾建立了光滑四流形的Donaldson不变量与Seiberg-Witten不变量之间的关系。在这篇综述文章中，我们描述了通过PU(2)=SO(3)单极模空间作为Donaldson模空间（反自对偶SO(3)联络）与U(1)单极模空间之间的余维数来证明这一关系的方案。我们概述了关于PU(2)单极的一些横截性和Uhlenbeck紧致性结果，以及一些用Seiberg-Witten不变量表示Donaldson不变量的计算。我们简要介绍了有关粘合理论的问题，重点讨论了一些特定于PU(2)单极的分析困难及其在PU(2)单极程序中的应用，以证明Donaldson和Seiberg-Witten不变量之间的关系。 显示英文摘要

摘要： Using quantum field-theoretic arguments, Witten has established a relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. In this survey article, we describe the program to prove this relation using a moduli space of PU(2) = SO(3) monopoles as a cobordism between the Donaldson moduli space of anti-self-dual SO(3) connections and moduli spaces of U(1) monopoles. We provide an overview of some of our transversality and Uhlenbeck compactness results for PU(2) monopoles, along with some of our calculations of Donaldson invariants in terms of Seiberg-Witten invariants. We give a brief outline of issues concerning the gluing theory, focussing on some of the analytical difficulties that are particular to PU(2) monopoles, and its application to the PU(2) monopole program to prove the relation between Donaldson and Seiberg-Witten invariants.