Geodesic
The dynamics of $\operatorname{Aut}(F_n)$ on redundant representations
Tsachik Gelander1 orcid ; Yair N. Minsky2 orcid
1The Hebrew University of Jerusalem, Israel
2Yale University, New Haven, United States
Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 557-576

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DOI

We study some dynamical properties of the canonical Aut(Fn​)-action on the space Rn​(G) of redundant representations of the free group Fn​ in G, where G is the group of rational points of a simple algebraic group over a local field. We show that this action is always minimal and ergodic, confirming a conjecture of A. Lubotzky. On the other hand for the classical cases where G=SL2​(R) or SL2​(C) we show that the action is not weak mixing, in the sense that the diagonal action on Rn​(G)2 is not ergodic.
DOI : 10.4171/ggd/197
Classification : 20-XX, 22-XX, 37-XX, 57-XX
Mots-clés : Aut(Fn​), character varieties, algebraic groups, 3-dimensional topology, dynamical decomposition, redundant representation, ergodicity

Tsachik Gelander  1   ; Yair N. Minsky  2

1 The Hebrew University of Jerusalem, Israel
2 Yale University, New Haven, United States 
Tsachik Gelander; Yair N. Minsky. The dynamics of $\operatorname{Aut}(F_n)$ on redundant representations. Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 557-576. doi: 10.4171/ggd/197
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     title = {The dynamics of $\operatorname{Aut}(F_n)$ on redundant representations},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/197/}
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