On dynamics of Out(F_n) on PSL(2,C) characters

Abstract

This note introduces and studies an open set of PSL(2,C) characters of a nonabelian free group, on which the action of the outer automorphism group is properly discontinuous, and which is strictly larger than the set of discrete, faithful convex-cocompact (i.e. Schottky) characters. This implies, in particular, that the outer automorphism group does not act ergodically on the set of characters with dense image. Hence there is a difference between the geometric (discrete vs. dense) decomposition of the characters, and a natural dynamical decomposition.

References in corpus (4)

• Tameness of hyperbolic 3-manifolds
• Dense embeddings of surface groups
• Dynamics of Aut(Fn) Actions on Group Presentations and Representations
• Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties

Cited by in corpus (5)

• Locally homogeneous geometric manifolds
• Dynamics on the PSL(2,C)-character variety of a twisted I-bundle
• The Space of Geometric Limits of Abelian Subgroups of PSL2C
• Birational Kleinian groups
• Simple Anosov representations of closed surface groups