Mathematical Sciences: Low-Dimensional Topology, Geometry and Thin-Positions

数学科学：低维拓扑、几何和薄位

• 批准号: 9409743
• 负责人: Abigail Thompson
• 金额: $ 3万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9409743&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Low; Dimensional; Topology

9409743 Thompson This career advancement award supports mathematical research on problems arising in the fields of knot theory, minimal surface theory and the theory of 3-manifolds. The emphasis of this project is to explore an area at the border between low-dimensional topology and geometry via the concept of thin position. In knot theory, this concept was first introduced by D. Gabai and used to solve the long-standing property R conjecture. The analog to thin position in minimal surface theory has been studied extensively the H. Rubenstein; in particular, thin position proved to be the key to the solution to the recognition problem for the 3-sphere. The knot theoretic interpretation of thin position has recently been used to give an alternate proof of Rubenstein's theorem, confirming close connections between the two points of view. Pursuit of such linkage between two different areas promises to be extremely fruitful. The goals of this project are twofold; first, to acquire a deep understanding of minimal surface theory, particularly PL-minimal surface theory. Second, to exploit thin position, with the intent of using insights from knot theory to solve interesting questions in minimal surface theory and vice-versa. ***

小行星9409743 这个职业发展奖支持在纽结理论，极小曲面理论和三维流形理论领域出现的问题的数学研究。 本计画的重点是借由薄位置的概念来探索低维拓扑与几何之间的边界区域。 在纽结理论中，这一概念首先由D. Gabai和用于解决长期存在的性质R猜想。 极小曲面理论中的薄面位置的模拟已经得到了广泛的研究.特别是，薄的位置被证明是解决3-球识别问题的关键。 纽结理论的解释薄的位置最近已被用来给另一个证明鲁宾斯坦定理，确认密切联系之间的两个观点。 在两个不同领域之间寻求这种联系，肯定会取得丰硕成果。 这个项目的目标是双重的;第一，深入了解极小曲面理论，特别是PL极小曲面理论。 第二，利用薄的位置，目的是使用结理论的见解来解决最小曲面理论中的有趣问题，反之亦然。 ***