Seiberg-Witten and Gromov invariants of symplectic 4-orbifolds and some applications

辛 4 环折的 Seiberg-Witten 和 Gromov 不变量及一些应用

• 批准号: 0638983
• 负责人: Weimin Chen
• 金额: --
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-02-28 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0638983&HistoricalAwards=false
• 关键词: Seiberg; Witten; Gromov; invariants; symplectic

DMS-0304956Weimin ChenThe Principal Investigator plans to continue his work in gaugetheory and symplectic, low-dimensional topology. More concretely,he plans to study the following problems: (1) general properties offinite groups of symplectomorphisms of a symplectic 4-manifold,(2) whether a symplectic circle action on a 6-dimensional manifoldis Hamiltonian if its fixed-point set is non-empty and finite, and(3) general, global restrictions on the occurrence of quotient singularitiesin an algebraic surface. A unifying theme in these studies is a theory,yet to be developed in this project, on the Seiberg-Witten and Gromovinvariants of a symplectic 4-orbifold, which will be built on andsubstantially extend the related fundamental work of Taubes onsymplectic 4-manifolds.A 4-dimensional orbifold is a space which locally looks like the space-time we all live in, except that there is a certain degree of ambiguity caused bya finite symmetry occured locally. Many examples of this kind of space can befound easily and naturally in Mathematics (e.g. topology and geometry) as wellas models in Theoretical Physics (e.g. orbifold string theory). The proposedresearch seeks to understand a fundamental duality in a 4-dimensional orbifoldbetween a certain type of fields that are distributed all over the space and a certaintype of worldsheet that is wiped out by a collection of strings in the space whichis condensed in a 2-dimensional subspace. When there is no such ambiguity of finite symmetries, such a duality is well-understood, and is a fundamental piece ofmathematics.

DMS-0304956 Weimin Chen首席研究员计划继续他在规范理论和辛，低维拓扑学方面的工作。更具体地说，他计划研究以下问题：（1）一般性质的有限群的辛同胚的辛4流形，（2）是否一个辛圈行动的6维流形哈密尔顿如果其不动点集是非空的和有限的，和（3）一般的，全球性的限制发生商singularities在代数曲面。这些研究中的一个统一主题是关于辛4-orbifold的Seiberg-Witten和Gromovin变体的理论，该理论将建立在Taubes关于辛4-流形的相关基本工作的基础上，并在很大程度上扩展。除了存在由局部发生的有限对称性引起的一定程度的模糊性之外。 这种空间的许多例子可以在数学（例如拓扑学和几何学）以及理论物理学（例如轨道弦理论）中很容易和自然地找到。 拟议的研究旨在理解一个基本的二元性在一个四维orbifold之间的某种类型的领域，分布在整个空间和某种类型的世界片，被消灭的一个收集弦的空间，这是凝聚在一个2维子空间。当有限对称性不存在这种模糊性时，这种对偶性就很容易理解，并且是数学的一个基本部分。