JournalsggdVol. 7, No. 3pp. 557–576

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

  • Tsachik Gelander

    The Hebrew University of Jerusalem, Israel
  • Yair N. Minsky

    Yale University, New Haven, United States
The dynamics of $\operatorname{Aut}(F_n)$ on redundant representations cover
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Abstract

We study some dynamical properties of the canonical Aut(Fn)\mathrm{Aut}(F_n)-action on the space Rn(G)\mathcal{R}_n(G) of redundant representations of the free group FnF_n in GG, where GG 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)G=\mathrm{SL}_2(\mathbb{R}) or SL2(C)\mathrm{SL}_2(\mathbb{C}) we show that the action is not weak mixing, in the sense that the diagonal action on Rn(G)2\mathcal{R}_n(G)^2 is not ergodic.

Cite this article

Tsachik Gelander, Yair N. Minsky, The dynamics of Aut(Fn)\operatorname{Aut}(F_n) on redundant representations. Groups Geom. Dyn. 7 (2013), no. 3, pp. 557–576

DOI 10.4171/GGD/197