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.

在代数拓扑结构中，广义的共同体理论已成为将拓扑问题转化为代数问题的恰当工具，可以在其中期望进行计算。 代数结构酮可以提取越多，越好。 在过去的30年左右的时间里，人们对以复杂导向的共同体学理论进行了扩展的开发，这些理论允许人们利用现有的富有正式群体法律的代数机制。 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作为距离和角度。 甜甜圈被视为等同于咖啡杯的备用例子，因为一个人可以将其呈现到另一个，而不会撕裂或粘合，如果它们是塑料的，但不等于没有手柄的杯子，因为孔会消失。 代数拓扑试图转换人们可以解决的代数问题。 一种强大的现代工具，是一个复杂的共同体学理论的概念，这是拟议的为期4天会议的重点。 这次会议旨在更广泛地宣传该领域的现状及其结果。