This award is a one-year renewal of an award to Professor Slawomir Kwasik and a graduate student of Tulane University to support collaboration in mathematics research with Professor Bjorn Jahren and others of the Department of Mathematics of the University of Oslo, Norway. The research studies the relationship between algebraic K-theory and pseudo-isotopy of manifolds, and applies new methods employing Waldhausen's A-theory to study various geometric questions concerning the topology of 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. There is still a great deal of interest in research in the above areas. Significant progress has already been made in the algebraic aspects of these theories, but work is still new on 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 as he continues to strengthen the research with his Norwegian counterpart. Dr. Kwasik and his collaborator have made strong progress on the original research goals, and will be able to complete those goals with the additional year's funding.