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.
