Essential Surfaces in Knot Exteriors: The Lopez Conjecture

提案ID：DMS-9978071提案标题：结外部的表面：洛佩斯猜想。主要研究者：William H.中文摘要：这个项目涉及一个特殊的学期在斯坦福大学和美国数学研究所汇集了一个团队的四名高级研究员，两名博士后研究员和两名高级研究生的紧张和合作的研究结外部的基本表面。在过去的二十年里，两名高级研究人员一直在研究一个项目，通过结外部基本表面的特性来检测某些结。他们的方法已经非常成功地识别这些属性，但没有导致方法，使人们能够实现这样的结。另外两名高级研究人员在过去三年中开发了实现具有有趣特性的结的新方法。这个项目将把这两种方法结合起来，以解决这一领域的数学研究中最突出的问题之一。低维拓扑汇集了数学研究的许多领域，并为所有数学的互动和进步提供了一个共同的基础。它为大多数物理现象提供了一个自然的几何模型。这一领域的研究对计算几何、拓扑学和复杂性理论做出了重要贡献。它在物理学、计算机可视化和医学建模中具有重要意义。

Proposal ID: DMS-9978071Proposal Title: Surfaces in knot exteriors: The Lopez Conjecture.Principal Investigator: Dr. William H. JacoAbstract: This project involves a Special Semester at Stanford University and The American Institute of Mathematics bringing together a team of four senior investigators, two postdoctoral fellows and two advanced graduate students for an intense and collaborative study of essential surfaces in knot exteriors. Two of the senior investigators have been working on a program over the past two decades to detect certain knots by properties of essential surfaces in the knot exterior. Their methods have been very successful in identifying such properties but do not lead to methods that will enable one to realize such knots. The other two senior investigators have in the last three years developed new methods for realizing knots having interesting properties. This project will bring these two methods together to address one of the most outstanding problems in this area of mathematical research.Low-dimensional topology brings together many areas of mathematical research and provides a common ground for interaction and advance across all of mathematics. It provides a natural geometric model of most physical phenomena. Research in this area is making significant contribution to computational geometry and topology and complexity theory. It has consequences in physics, computer visualization and medical modeling.