Topology of Smooth 4-Manifolds

光滑4流形拓扑

• 批准号: 0204579
• 负责人: Selman Akbulut
• 金额: $ 21.32万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-01 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0204579&HistoricalAwards=false
• 关键词: Topology; Smooth; Manifolds

DMS-0204579Selman AkbulutProposer plans to investigate the topology of smooth 4-manifolds by decomposing them into Stein pieces which are easy to understand (since they turn out to be Lefschetz fibrations over the 2-disk). He would like use the techniques of complex and symplectic manifolds to understand the restriction this decomposition imposes to the topology of the original manifold. Proposer hopes to apply these techniques to attack some unsolved problems of 4-dimensional topology, such as finding 4-dimensional fake s-cobordisms, and to the problem of constructing a fake S^3 x S^1. Proposer also plans to work on the topological problems arising from complex algebraic geometry, such as problems coming from the complex conjugation, branched covers and the curve counting problem in real algebraic geometry.Proposer plans to investigate structure of 4-dimensional manifolds by decomposing them into pieces that are topologically easier to understand (4-manifolds are spaces which locally look like 4-dimensional Euclidean space-time we live in). These smaller pieces carry certain `natural complex structures' which analytical techniques apply. By these techniques Principal investigator hopes to construct certain 4-manifolds believed to exists but not yet have been found. One of the reasons 4-manifolds are of interest is because of the physicists model of the 10-dimensional universe which consists of a 4-dimensional space-time plus 6-dimensional complex piece.

DMS-0204579Selman AkbulutProposer计划通过将它们分解为易于理解的Stein片来研究光滑的4个manifolds的拓扑拓扑（因为事实证明它们是2盘上的Lefschetz纤维）。他想利用复杂和符号歧管的技术来理解这种分解对原始流形的拓扑施加的限制。建议者希望应用这些技术来攻击一些四维拓扑的未解决问题，例如寻找4维假S- bobordism，以及构建假S^3 x S^1的问题。提议者还计划处理由复杂的代数几何形状引起的拓扑问题，例如来自复杂的共轭，分支覆盖的问题，分支覆盖和曲线计数问题，曲线范围的计划来调查四维流形的结构，使它们分解为四维流形的零件，这些零件可以像拓扑相位（4-跨度），从而可以拓扑（4-跨性别），这是4-型号的距离（4- manifim of Spoce），这是4-型号的范围，这些距离是4-型号的范围。我们住在）。这些较小的零件具有适用分析技术的某些“天然复杂结构”。通过这些技术，首席研究人员希望构建某些被认为存在但尚未发现的4个manifolds。 4个manifolds引起的原因之一是由于10维宇宙的物理学家模型，该模型由4维时空加6维复合物组成。