12/11/2008

Yair Minsky
Yale University

Primitive-stable representations of the free group

Automorphisms of the free group F_n act on its representations into a given group G. When G is a simple compact Lie group and n>2, Gelander showed that this action is ergodic. We consider the case G=PSL(2,C), where the variety of (conjugacy classes of) representations has a natural invariant decomposition, up to sets of measure 0, into discrete and dense representations. This turns out NOT to be the relevant decomposition for the dynamics of the outer automorphism group. Instead we describe a set called the "primitive-stable" representations containing discrete as well as dense representations, onwhich the action is properly discontinuous.