Mathematical Sciences: Topology of Real Algebraic Varieties and 4-Manifolds

数学科学：实代数簇和 4-流形的拓扑

• 批准号: 8901739
• 负责人: Selman Akbulut
• 金额: $ 5.03万
• 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: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901739&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topology; Real; Algebraic

The investigator will continue his longstanding project with Henry King of the University of Maryland to formulate topological characterizations of manifolds which can support the structure of real algebraic varieties. The subgroup of algebraic cycles within the homology figures prominently in this work, and surprisingly, this year, they have shown that certain obstructions vanish if one allows singular varieties. A second direction for the investigator's research involves gauge theory and its role in the study of 4-manifolds. A final direction concerns the question of Nash: do all closed smooth manifolds have rational structure?

这位研究人员将继续他与马里兰大学的亨利·金的长期项目，以制定能够支持实代数簇结构的流形的拓扑刻画。同调中的代数圈的子群在这项工作中表现得尤为突出，令人惊讶的是，今年，他们已经证明，如果一个人允许奇异变元，某些障碍就会消失。研究者研究的第二个方向涉及规范理论及其在四维流形研究中的作用。最后一个方向涉及纳什的问题：所有的闭光滑流形都有合理的结构吗？