Bernhard Kroen, University of Vienna and The City College of New York

Abstract:
Joint with M.J. Dunwoody. We generalize structure tree theory (book Dicks & Dunwoody "Groups acting on Graphs") from the principle of removing finite sets of edges to removing finite sets of vertices. As application we obtain generalizations of Stallings' theorem about ends of groups and a theorem which is close to Kropholler's conjecture on group splittings.