Cut-and-paste contact topology

剪切和粘贴接触拓扑

• 批准号: 0406158
• 负责人: William Kazez
• 金额: --
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0406158&HistoricalAwards=false
• 关键词: Cut; paste; contact; topology

The pioneering works of Bennequin and Eliashberg from the 1980s and the 1990s have shown that, among all contact structures, the tight ones best reflect the topology of the ambient space. Only in the past decade have sufficient tools been developed to allow many of the basic classification questions in the subject to be attacked. The PI proposes joint work with Honda and Mati\'c to analyze the contact topology of Haken manifolds using cut-and-paste techniques. Important outgrowths of this investigation include constructions of tight contact structures in Haken homology spheres, extensions of the relationship with foliation theory to laminations and hyperbolic manifolds, and an understanding of the interplay between the subsurface complex and contact structures on a product.Three-dimensional manifolds are modeled on the three-dimensional space we live in. Contact and symplectic topology were originally motivated by questions of physicists working in classical mechanics and thermodynamics. They arise in a surprisingly broad array of applied situations ranging from fluid flows to the manufacture of projection screen televisions. The proposed research has the potential to produce new results applicable to these fields.

Bennequin和Eliashberg在20世纪80年代和90年代的开创性工作表明，在所有接触结构中，紧密的接触结构最能反映周围空间的拓扑结构。只是在过去的十年里，才开发出足够的工具，使该主题中的许多基本分类问题得到解决。PI建议与本田和Mati\'c联合工作，使用剪切和粘贴技术分析哈肯流形的接触拓扑结构。这项研究的重要成果包括在哈肯同调球的紧密接触结构的建设，与叶理理论的关系，叠层和双曲流形的扩展，并了解之间的相互作用的地下复杂和接触结构的product.Three-dimensional流形的三维空间，我们生活在建模。 接触和辛拓扑最初是由研究经典力学和热力学的物理学家提出的问题所激发的。它们出现在从流体流动到投影屏幕电视制造的一系列令人惊讶的广泛应用情况中。拟议的研究有可能产生适用于这些领域的新成果。