U.S.-Norway Cooperative Research in Topology

美国-挪威拓扑学合作研究

• 批准号: 9505890
• 负责人: Slawomir Kwasik
• 金额: $ 1.83万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505890&HistoricalAwards=false
• 关键词: U.S.; Norway; Cooperative; Research; Topology

This award supports Professor Slawomir Kwasik and a graduate student of Tulane University to collaborate in mathematics research with Professor Bjorn Jahren and others of the Department of Mathematics of the University of Oslo, Norway. They will study the relationship between algebraic K-theory and pseudo-isotopy of manifolds, and they will apply new methods employing Waldhausen's A-theory to study various geometric questions concerning the topology of manifolds. They will also use gauge theoretic techniques to gain a new insight into the pseudo-isotopies of low-dimensional manifolds. The research is strengthened by the experience of Dr. Kwasik in the more geometric aspects of pseudo-isotopy theory but relies primarily on the expertise and new approach developed by Professor Jahren. Recently introduced mathematical techniques have provided powerful tools to perform specific algebraic calculations. This has led to a surge of interest in research in the above areas. Significant progress has already been made in the algebraic aspects of these theories, but work is just beginning in the geometrical side. Indeed the strongest centers pursuing this research are in Northern Europe, and the proposed collaboration with a Norwegian group will provide access to the latest research developments for Dr. Kwasik and his student. Another attractive feature is the involvement of two well regarded Polish mathematicians who have made contributions to the same area of mathematics. They plan to synchronize visits to Norway with Dr. Kwasik. This will provide to US investigators insights and links to Eastern European workers in this field.

该奖项支持Slawomir Kwasik教授和Tulane University的研究生，与Bjorn Jahren教授和挪威奥斯陆大学数学系的其他人进行数学研究合作。 他们将研究代数K理论与流形的伪异常之间的关系，并将采用使用Waldhausen的A理论来研究有关歧管拓扑的各种几何问题的新方法。 他们还将使用量规理论技术来获得对低维歧管的伪异构体的新见解。 夸西克博士在伪异位理论的几何方面的经验增强了这项研究，但主要依赖于Jahren教授开发的专业知识和新方法。 最近引入的数学技术提供了执行特定代数计算的强大工具。 这导致了上述领域对研究的兴趣激增。 这些理论的代数方面已经取得了重大进展，但是工作才始于几何方面。 实际上，追求这项研究的最强中心是在北欧，与挪威团体的拟议合作将为Kwasik博士及其学生提供最新的研究发展。 另一个有吸引力的功能是，两位受人尊敬的波兰数学家的参与，他们为同一数学领域做出了贡献。 他们计划与夸西克博士同步挪威访问。 这将为美国调查人员的见解和与该领域东欧工人的联系。