Cocycle superrigidity from higher rank lattices to Out(F_N) - Centre Henri Lebesgue Accéder directement au contenu
Article Dans Une Revue Journal of modern dynamics Année : 2022

Cocycle superrigidity from higher rank lattices to Out(F_N)

Camille Horbez
Jean Lécureux

Résumé

We prove a rigidity result for cocycles from higher rank lattices to Out(F N) and more generally to the outer automorphism group of a torsion-free hyperbolic group. More precisely, let G be either a product of connected higher rank simple algebraic groups over local fields, or a lattice in such a product. Let G X be an ergodic measure-preserving action on a standard probability space, and let H be a torsion-free hyperbolic group. We prove that every Borel cocycle G × X → Out(H) is cohomologous to a cocycle with values in a finite subgroup of Out(H). This provides a dynamical version of theorems of Farb-Kaimanovich-Masur and Bridson-Wade asserting that every morphism from G to either the mapping class group of a finite-type surface or the outer automorphism group of a free group, has finite image. The main new geometric tool is a barycenter map that associates to every triple of points in the boundary of the (relative) free factor graph a finite set of (relative) free splittings.
Fichier principal
Vignette du fichier
2005.07477.pdf (529.87 Ko) Télécharger le fichier
Loading...

Dates et versions

hal-02611060 , version 1 (18-11-2020)

Identifiants

Citer

Vincent Guirardel, Camille Horbez, Jean Lécureux. Cocycle superrigidity from higher rank lattices to Out(F_N). Journal of modern dynamics, 2022, 18, pp.291-344. ⟨10.3934/jmd.2022010⟩. ⟨hal-02611060⟩
86 Consultations
76 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More