Primitive-stable representations of the free group

Primitive-stable representations of the free group

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Yair Minsky, Yale University
Fine Hall 314

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.