Topology of Smooth 4-Manifolds

光滑4流形拓扑

• 批准号: 9971440
• 负责人: Selman Akbulut
• 金额: $ 6.33万
• 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: 1999
• 资助国家: 美国
• 起止时间: 1999-07-15 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971440&HistoricalAwards=false
• 关键词: Topology; Smooth; Manifolds

Proposal: DMS-9971440Principal Investigator: Selman AkbulutAbstract: The principal investigator will investigate the topology of smooth 4-manifolds. By decomposing smooth manifolds into complex pieces, he will use the techniques of complex and symplectic manifolds to understand the restriction this decomposition imposes on the topology of smooth 4-manifolds. The principal investigator hopes to apply the techniques from the solution of the `Scharlemann problem' and Fintushel-Stern constructions to the problem of constructing 4-dimensional fake s-cobordisms, and to the problem of constructing a fake copy of `three-sphere crossed with circle'. He would like to study topology of Horikawa surfaces and hopes to give affirmative answers to various branched covering conjectures.The principal investigator intends to study generalized 4-dimensional spaces (4-manifolds); he hopes to find new ones. These spaces arise naturally in physics: relativity (space-time) and quantum field theories. Recently there have been exciting developments about the structure of these spaces coming from the ideas of physics, but we still don't know if certain basic exotic 4-manifolds could exist. If they exist they will be basic building blocks of the known ones. We would like to investigate possible constructions which could give their existence.

提案：DMS-9971440原理研究人员：Selman Akbulutabstract：首席研究员将调查光滑4个manifolds的拓扑。 通过将光滑的歧管分解为复杂的碎片，他将使用复杂和符号歧管的技术来理解这种分解的限制对光滑的4个manifolds的拓扑构成。 首席研究人员希望将“ Scharlemann问题”和Fintushel-Sertther构造的解决方案应用于构建四维假S-cobordism的问题，以及构建“与Circle交叉的三个速度交叉”的假副本的问题。他想研究Horikawa表面的拓扑结构，并希望为各种分支覆盖的猜想提供肯定的答案。他希望找到新的。这些空间自然出现在物理学：相对论（时空）和量子场理论中。 最近，关于这些空间的结构来自物理学思想的结构令人兴奋，但我们仍然不知道某些基本的异国情调的4个manifolds是否存在。如果它们存在，它们将是已知的基本基础。我们想调查可能赋予其存在的可能结构。