Workshop in Knot Concordance and Homology Cobordism

1957年，r·h·福克斯（R. H. Fox）和j·米尔诺（J. Milnor）提出了一个开创性的观点，即奇点链接的一致性类阻碍了奇点的移除。结点的一致性和理解奇点的激励目标仍然是拓扑和代数几何的核心。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的一致性。Cochran-Orr-Teichner引入的n可解过滤，以及许多作者随后建立（一半）分级商的非平凡性的工作，使人们认识到，也许结的一致性是基本群可能允许的最复杂的。一个会议将于2010年7月19日至23日在卫斯理大学举行，汇集了各种各样的研究人员和学生，他们的工作与结的一致性有关。结理论是对三维空间中结曲线的研究。结曲线的研究在生物学和物理学中有着重要的应用。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与4空间中的圆盘结合。这一激励问题是结协调研究的基础。结和谐诞生于4流形的研究，并仍然是其最容易接近的后代。

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.