Workshop in Knot Concordance and Homology Cobordism

1957年，R.H.福克斯和J.米尔纳提出了一个开创性的观点，即奇点链接的和谐性类别阻碍了它的移除。纽结的一致性和理解奇点的激励目标仍然是拓扑学和代数几何的核心。在过去的10年里，我们看到我们对纽结和纽结和谐的认识取得了巨大的进步。Cochran-Orr-Teichner提出的n-可解滤子，以及随后许多作者建立(一半)分次商的非平凡性的工作，导致人们认识到，也许纽结调和是像基本群可能允许的那样完全复杂的。一场会议将于2010年7月19日至23日在卫斯理大学举行，与会的研究人员和学生的工作与纽结和谐法有关。纽结理论是对三维空间中纽结曲线的研究。结点曲线的研究在生物学和物理学中都有重要的应用。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4维空间中限制圆盘。这个激励问题是研究纽结协调性的基础。纽结一致性诞生于对4-流形的研究，至今仍是它最容易接近的产物。

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.