The topology and geometry of automorphism groups of free groups II

Free groups, free abelian groups and fundamental groups of

closed orientable surfaces are the most basic and well-understood

examples of infinite discrete groups. The automorphism groups of

these groups, in contrast, are some of the most complex and intriguing

groups in all of mathematics. In these lectures I will concentrate

on groups of automorphisms of free groups, while drawing analogies

with the general linear group over the integers and surface mapping

class groups. I will explain modern techniques for studying

automorphism groups of free groups, which include a mixture of

topological, algebraic and geometric methods.