The topology and geometry of automorphism groups of free groups II
Abstract
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.