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

数学科学：实代数集和 4-流形的拓扑

• 批准号: 9102518
• 负责人: Selman Akbulut
• 金额: $ 9.3万
• 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: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102518&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topology; Real; Algebraic

This research project consists of two main parts, concerning (1) the topology of real algebraic sets, and (2) the topology of smooth 4-manifolds. The first part will build on the investigator's success (together with Henry King of the University of Maryland) in settling an old conjecture of John Nash. The second part will focus on the construction of fake smooth structures on 4-manifolds, particularly their detection by means of such new invariants as Floer homology and the still newer invariants of Turaev-Reshetikhin-Witten coming from quantum groups. Both parts of this project concern themselves with very natural objects which are ubiquitous in mathematics and mathematical physics. Four-manifolds are cosmologically important, since we live in a manifold of three space dimensions plus one time dimension.

该研究项目包括两个主要部分， (1)真实的代数集的拓扑;（2） 光滑四维流形 第一部分将建立在 调查员的成功（连同亨利国王） 马里兰州大学）在解决一个古老的猜想约翰 纳什 第二部分将重点放在假冒伪劣商品的建设上 4流形上的光滑结构，特别是它们的检测 手段等新的不变量作为弗洛尔同源性和仍然 Turaev-Reshetikhin-维滕的量子不变量 组 这个项目的两个部分都非常关注 数学中无处不在的自然对象， 数学物理 四维流形在宇宙学上 这很重要，因为我们生活在三维空间的流形中 加上一个时间维度