U.S.-Norway Cooperative Research in Topology

该奖项支持Slaomeir Kwasik教授和杜兰大学的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。他们将研究流形的代数K-理论和伪同余之间的关系，并将应用Waldhausen的A-理论的新方法来研究与流形拓扑有关的各种几何问题。他们还将使用规范理论技术来获得对低维流形的伪同位素的新见解。夸西克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，但主要依赖于贾伦教授开发的专业知识和新方法。最近引入的数学技术为执行特定的代数计算提供了强大的工具。这导致了人们对上述领域研究的兴趣激增。这些理论在代数方面已经取得了重大进展，但在几何方面的工作才刚刚开始。事实上，从事这项研究的最强大的中心在北欧，拟议中的与挪威团队的合作将为夸西克博士和他的学生提供接触最新研究进展的途径。另一个吸引人的特点是两位在同一数学领域做出贡献的著名波兰数学家的参与。他们计划与夸西克博士同步访问挪威。这将为美国调查人员提供洞察力，并与该领域的东欧工人建立联系。

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.