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教授和杜兰大学的一名研究生与挪威奥斯陆大学数学系的Bjorn Jahren教授和其他人合作进行数学研究。 他们将研究代数K-理论和伪合痕的流形之间的关系，他们将应用新的方法采用瓦尔德豪森的A-理论研究各种几何问题有关的拓扑流形。 他们还将使用规范理论的技术，以获得一个新的洞察到伪同位素的低维流形。 Kwasik博士在伪同位素理论的更多几何方面的经验加强了这项研究，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强大的工具来执行特定的代数计算。 这导致了对上述领域研究的兴趣激增。 重大进展已经取得了代数方面的这些理论，但工作才刚刚开始在几何方面。 事实上，从事这项研究的最强大的中心在北方欧洲，与挪威小组的拟议合作将为Kwasik博士和他的学生提供最新的研究进展。 另一个有吸引力的特点是参与两个备受推崇的波兰数学家谁作出了贡献，同一领域的数学。 他们计划与Kwasik博士同步访问挪威。 这将为美国调查人员提供见解，并与该领域的东欧工作者建立联系。