Complex Cobordisom in Homotopy Theory; Its Impact and Prospects

同伦理论中的复杂协调；

• 批准号: 0634227
• 负责人: John Michael Boardman
• 金额: $ 2.8万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-11-15 至 2008-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0634227&HistoricalAwards=false
• 关键词: Complex; Cobordisom; Homotopy; Theory; Its

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.

在代数拓扑中，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。可以提取的代数结构越多越好。在过去30年左右的时间里，我们看到了面向复上同调理论家族的广泛发展，它使我们能够利用现有的形式群定律的丰富代数机制。应用程序包括拓扑中的许多深刻的结果。然而，大部分工作是在相当少的几个中心进行的，拟议的为期四天的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。拓扑学是研究几何物体的性质，如球体、环面和其他表面，以及高维的类似物，它们不依赖于距离和角度等概念。一个典型的例子是，一个甜甜圈被视为相当于一个咖啡杯，因为如果它们足够塑料，一个可以变形成另一个，而不会撕裂或粘上，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可以求解的代数问题。一个强大的现代工具是面向复杂上同理论的概念，这是提议的为期4天的会议的重点。这次会议的目的是更广泛地传播该领域的现状及其成果。