This award supplements support provided for Vogtmann's research under DMS-8702070 with K. S. Brown as principal investigator. It will enable her to take part in the special year in combinatorial group theory at the Mathematical Sciences Research Institute, Berkeley, California, during the spring of 1989. The general area of research is in topological and geometric methods in group theory. The specific problems concern various subgroups of the group of outer automorphisms of a finitely generated free group, and related groups. The idea is to adapt the very beautiful and powerful techniques used in the study of arithmetic groups to the study of these groups. One basic tool is the action of the group of outer automorphisms of a free group on a contractible space developed by the principal investigator and Marc Culler.
