Topology Autmsm

This book re-examines J. H. C. Whitehead's 1936 papers on free groups, from the viewpoint of categories of homotopy equivalences of combinatorial graphs. Buildings are introduced and shown to have high connectivity. The defining relations of the automorphism group of a finitely generated free group F are analyzed geometrically. Whitehead's problem, that is to decide whether two finitely generated subgroups of F are equivalent by an automorphism of F, is solved effectively, and McCool's finiteness results on stabilizers are generalized.