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，广义上同调理论已成为将拓扑问题转化为代数问题的强大工具，人们可以在其中进行计算。 能够提取的代数结构越多越好。 在过去 30 年左右的时间里，复向上同调理论家族得到了广泛的发展，这使得人们能够利用现有的丰富的形式群律代数机制。 应用包括拓扑学中的许多深刻的成果。然而，大部分工作是在相当少数的中心进行的，拟议的为期 4 天的会议旨在向更广泛的受众传播该领域的现状，包括出版拓扑学是对球体、环面和其他表面以及高维类似物等几何对象属性的研究，这些属性不依赖于距离和角度等概念。 一个常见的例子是，甜甜圈被视为等同于咖啡杯，因为如果它们具有足够的塑料，则可以将一个甜甜圈变形为另一个，而无需撕裂或粘合，但不等同于没有手柄的杯子，因为孔不会消失。 代数拓扑旨在将拓扑问题转化为可以解决的代数问题。 一个强大的现代工具是复向上同调理论的概念，这是拟议的为期 4 天的会议的焦点。 本次会议旨在更广泛地传播该领域的现状及其成果。