Workshop in Knot Concordance and Homology Cobordism

结一致性和同源协调研讨会

• 批准号: 1042053
• 负责人: Constance Leidy
• 金额: $ 1.89万
• 依托单位: Wesleyan University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-15 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1042053&HistoricalAwards=false
• 关键词: Workshop; Knot; Concordance; Homology; Cobordism

In 1957, R. H. Fox and J. Milnor introduced the seminal idea that the concordance class of the link of a singularity obstructs its removal. Both concordance of knots, and the motivating goal of understanding singularities remain central to topology and algebraic geometry. In the last 10 years we have seen tremendous advances in our knowledge of knot and link concordance. The introduction of the n-solvable filtration, by Cochran-Orr-Teichner, and the subsequent work of many authors establishing the non-triviality of (half of) the graded quotients has led to the realization that perhaps knot concordance is as fully complicated as the fundamental group might allow. A conference will be held at Wesleyan University, July 19-23, 2010, to bring together a variety of researchers and students whose work connects to knot concordance.Knot theory is the study of knotted curves in 3-space. The study of knotted curves has important applications in biology and physics. A fundamental question in knot theory and low-dimensional topology is when such a curve bounds a disk in 4-space. This motivating question is the foundation for the study of knot concordance. Knot concordance was born of the study of 4-manifolds and remains its most accessible progeny.

1957年，R. H.福克斯和米尔诺提出了一个开创性的想法，即奇点的联系的和谐类阻碍了它的去除。纽结的和谐性和理解奇点的动机目标仍然是拓扑学和代数几何的核心。在过去的10年里，我们已经看到了巨大的进步，我们的知识结和链接一致性。由Cochran-Orr-Teichner引入的n-可解过滤，以及许多作者随后建立（一半）分次因子的非平凡性的工作，使人们认识到，也许结协调是完全复杂的，因为基本群可能允许。2010年7月19日至23日，卫斯理大学将举行一次会议，汇集各种研究人员和学生，他们的工作与结一致性有关。结理论是对三维空间中的打结曲线的研究。纽结曲线的研究在生物学和物理学中有重要的应用。纽结理论和低维拓扑学中的一个基本问题是这样的曲线何时在四维空间中界定一个圆盘。这个激励问题是研究结一致性的基础。纽结和谐诞生于四维流形的研究，并且仍然是它最容易获得的后代。