The problems addressed by this research project are in the area of geometric topology. Their common theme centers on automorphism groups of various kinds of spaces. Primarily these spaces are manifolds of various dimensions, but also addressed here are issues concerning more general kinds of spaces, such as trees or complexes. What kinds of groups can effectively act on such spaces? What does the space tell one about the group? This leads to focusing on the groups themselves, and how they decompose, or how they can act on other simple spaces, for example, trees. It is worthwhile to understand the topology of various possible classifying spaces for these groups, and what they look like at infinity. In addition to the principal investigator, R. D. Edwards, two faculty associates, Mladen Bestvina and Geoffrey Mess, and two advanced graduate students are involved. The work of all participants focuses on abstract spaces and the application of algebraic methods to their classification and understanding. There has been an enormous amount of activity in all of these areas in recent years, and there is much opportunity for further progress.
