Mathematical Sciences: Homotopy Spheres and Other Smooth 4-Manifolds

数学科学：同伦球和其他光滑 4 流形

• 批准号: 8801135
• 负责人: Robert Gompf
• 金额: $ 1.54万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801135&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Homotopy; Spheres; Other

The topology of smooth 4-dimensional manifolds will be studied by classical techniques as well as by new methods from gauge theory. For example, a certain infinite family of homotopy 4-spheres will be studied. This should provide evidence for or against the 4-dimensional smooth Poincare conjecture, one of the most notorious conjectures in topology.

光滑四维流形的拓扑将用经典方法和规范理论中的新方法来研究。例如，我们将研究一类无穷族的同伦4-球面。这应该为支持或反对4维光滑Poincare猜想提供证据，这是拓扑学中最臭名昭著的猜想之一。