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The dynamics of $\operatorname{Aut}(F_n)$ on redundant representations

Tsachik Gelander, Yair Minsky
2013 Groups, Geometry, and Dynamics  
We study some dynamical properties of the canonical Aut.F n /-action on the space R n .G/ of redundant representations of the free group F n in G, where G is the group of rational points of a simple algebraic  ...  We show that this action is always minimal and ergodic, confirming a conjecture of A. Lubotzky.  ...  An element of F n is primitive if it is a member of a free generating set. Whitehead gave the following property as part of an algorithm for deciding primitivity in F n : Basic Lemma (Whitehead) .  ... 
doi:10.4171/ggd/197 fatcat:5hpdwz2swzes7nmwnumqvpopz4