FRG: Topological Invariants of 3 and 4-Manifolds

FRG：3 和 4 流形的拓扑不变量

• 批准号: 0244622
• 负责人: Selman Akbulut
• 金额: --
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0244622&HistoricalAwards=false
• 关键词: FRG; Topological; Invariants; Manifolds

DMS-0244622Selman AkbulutThis is a Division of Mathematical Sciences Focused Research Group (FRG) award made under solicitation http://www.nsf.gov/pubs/2002/nsf02129/nsf02129.htmThe goal of this proposal is to find purely topological (continuous orcombinatorial) definitions of the invariants arising out ofSeiberg-Witten theory. These include the basic classes for4-dimensional manifolds, and the Oszvath-Szabo Floer homology for3-manifolds. Recent progress, in particular the striking results ofOzsvath and Szabo in the last two years, has brought Seiberg-Wittentheory seemingly close to topology, and a concerted effort by thisgroup may be able finish the task.This proposal falls under the larger topics of gauge theory and stringtheory, which are closely connected to and motivated by theoreticalphysics, in particular the attempt to unify the forces of nature.Low-dimensional bordism theory is the mathematical analogue of n+1dimensional quantum field theories, i.e. an n-dimensional space and1-dimensional time correspond to an (n+1)-dimensional bordism betweentwo n-dimensional manifolds. These bordisms can have extra structure,e.g. contact structures in odd dimensions and symplectic structures ineven dimensions. Progress in understanding the mathematicalunderpinnings of this sort of physics feeds back into betterunderstanding of the physics.

DMS-0244622Selman AkbulutThis is a Division of Mathematical Sciences Focused Research Group (FRG) award made under solicitation http://www.nsf.gov/pubs/2002/nsf02129/nsf02129.htmThe goal of this proposal is to find purely topological (continuous orcombinatorial) definitions of the不变的理论出现了。 其中包括4维流形的基本类别，以及3-manifolds的Oszvath-Szabo浮动同源性。 最近的两年中，最近的进步，特别是在过去的两年中的惊人结果，使塞伯格·胜利（Seiberg-Wittentheory）看似接近拓扑结构，而本组的一致努力可能能够完成任务。这一建议属于较大的量学理论和弦乐的主题，这些理论与策略紧密相关，这些主题与特定的态度相关，尤其是企图，尤其是范围，尤其是在理论上的态度，尤其是在理论上的态度。理论是n+1维量子场理论的数学类似物，即n维空间和1维时间对应于n维歧管的（n+1） - 维界的bordism。 这些狂热可以具有额外的结构，例如。奇数维度和符号结构中的接触结构不超过11​​个维度。 理解这种物理学的数学指南的进展可以使物理学的更好地理解。