The dynamics of Aut (Fn) on redundant representations

Tsachik Gelander, Yair Minsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We study some dynamical properties of the canonical Aut.Fn/-action on the space ℜn(G) of redundant representations of the free group F n in G, where G is the group of rational points of a simple algebraic group over a local field. We showthat this action is always minimal and ergodic, confirming a conjecture of A. Lubotzky. On the other hand for the classical cases where G D 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.

Original languageEnglish (US)
Pages (from-to)557-576
Number of pages20
JournalGroups, Geometry, and Dynamics
Volume7
Issue number3
DOIs
StatePublished - 2013

Keywords

  • 3-dimensional topology
  • Algebraic groups
  • Aut(Fn)
  • Character varieties
  • Dynamical decomposition
  • Ergodicity
  • Redundant representation

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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