Special Surfaces in Knot Complements

结补中的特殊表面

• 批准号: 0704207
• 负责人: Maggy Tomova
• 金额: $ 9.02万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-15 至 2008-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0704207&HistoricalAwards=false
• 关键词: Special; Surfaces; Knot; Complements

Tomova's research centers on Heegaard splittings of 3-dimensional manifolds and bridge surfaces for knots in manifolds. Given a knot in a closed 3-manifold, a bridge surface is a surface that decomposes the manifold into handlebodies and also cuts the knot into simple arcs. In the last year and a half Tomova has proven several important results about the behavior of bridge surfaces. She intends to extend and generalize her results and apply her work to several open problems in the area.With the discovery of the DNS molecule and the recent advent of string theory, the study of knots has come to the forefront of modern science. Knot Theory is a subarea of Topology which studies the properties of knotted strings and is the main area of interest of Maggy Tomova. Her study of knots also requires an understanding of 3-manifolds, objects that locally look like 3-dimensional space.

Tomova的研究中心Heegaard分裂的三维流形和桥梁表面的结在流形上。 给定封闭3-流形中的一个结，桥曲面是将流形分解为柄体并将结切割为简单弧线的曲面。在过去的一年半里，Tomova证明了关于桥梁表面行为的几个重要结果。随着DNS分子的发现和弦理论的出现，纽结的研究已经走到了现代科学的前沿。结理论是一个子领域的拓扑研究性质的打结字符串，是主要领域的兴趣玛吉Tomova。她的研究结还需要了解3-流形，物体局部看起来像三维空间。