Complex Cobordisom in Homotopy Theory; Its Impact and Prospects

在代数拓扑学中，广义上同调理论已经成为将拓扑问题转化为代数问题的有力工具，在代数问题中人们可以期望进行计算。 能提取的代数结构越多越好。 在过去的30年左右已经看到了广泛的发展家庭的复杂导向的上同调理论，其中一个挖掘到现有的丰富的代数机器的正式群法律。 拓扑学的应用包括拓扑学中许多深刻的结果。然而，大部分工作都发生在相当少的几个中心，拟议的4天会议旨在向更广泛的受众传播该领域的现状，包括出版会议记录。拓扑学是对几何对象（如球体、环面和其他表面）以及高维类似物的性质的研究，它不依赖于距离和角度等概念。 一个常见的例子是，甜甜圈被视为相当于一个咖啡杯，因为一个可以变形成另一个，而不会撕裂或粘合，如果它们有足够的可塑性，但不等同于一个没有把手的杯子，因为洞不会消失。 代数拓扑学试图将拓扑问题转化为人们可以解决的代数问题。 一个强有力的现代工具是面向复数的上同调理论的概念，这是拟议的4天会议的重点。 这次会议旨在更广泛地传播该领域的现状及其成果。

In algebraic topology, generalized cohomology theories have become apowerful tool for translating topological problems into algebraicproblems, where one can expect to do calculations. The more algebraic structureone can extract, the better. The last 30 years or so have seen extensivedevelopment of the family of complex-oriented cohomology theories, whichallow one to tap into the existing rich algebraic machinery of formalgroup laws. Applications include many profound results in topology.However, much of the work has taken place at a rather small number ofcenters, and the proposed 4-day conference is intended to disseminatethe present state of the field to a wider audience, including publicationof the proceedings of the conference.Topology is the study of those properties of geometric objects such asspheres, tori and other surfaces, and higher-dimensional analogues, thatdo not depend on such concepts as distance and angle. A stock exampleis that a donut is treated as equivalent to a coffee mug, as one can bedeformed into the other, without tearing or gluing, if they are plasticenough, but not equivalent to a cup without a handle, as the hole willnot go away. Algebraic topology seeks to convert topological problemsinto algebraic problems that one can solve. One powerful modern toolis the concept of a complex-oriented cohomology theory, which is thefocus of the proposed 4-day conference. This conference is intended todisseminate the present state of the field and its results more widely.