Geodesic
Out$(F_{n})$-invariant probability measures on the space of $n$-generated marked groups
Denis Osin1
1Vanderbilt University, Nashville, USA
Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 431-444

Voir la notice de l'article provenant de la source EMS Press

DOI

Let Gn​ denote the space of n-generated marked groups. We prove that, for every n≥2, there exist 2א0​ non-atomic, Out(Fn​)-invariant, mixing probability measures on Gn​. On the other hand, there are non-empty closed subsets of Gn​ that admit no Out(Fn​)-invariant probability measure. Acylindrical hyperbolicity of the group Aut(Fn​) plays a crucial role in the proof of both results. We also discuss model-theoretic implications of the existence of Out(Fn​)-invariant, ergodic probability measures on Gn​.
DOI : 10.4171/ggd/881
Classification : 20F65, 03C75, 20F67, 37A15
Mots-clés : space of marked groups, invariant measure, acylindrically hyperbolic group, elementary equivalence

Denis Osin  1

1 Vanderbilt University, Nashville, USA 
Denis Osin. Out$(F_{n})$-invariant probability measures on the space of $n$-generated marked groups. Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 431-444. doi: 10.4171/ggd/881
@article{10_4171_ggd_881,
     author = {Denis Osin},
     title = {Out$(F_{n})$-invariant probability measures on the space of~$n$-generated marked groups},
     journal = {Groups, geometry, and dynamics},
     pages = {431--444},
     year = {2025},
     volume = {19},
     number = {2},
     doi = {10.4171/ggd/881},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/881/}
}
TY  - JOUR
AU  - Denis Osin
TI  - Out$(F_{n})$-invariant probability measures on the space of $n$-generated marked groups
JO  - Groups, geometry, and dynamics
PY  - 2025
SP  - 431
EP  - 444
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/881/
DO  - 10.4171/ggd/881
ID  - 10_4171_ggd_881
ER  - 
%0 Journal Article
%A Denis Osin
%T Out$(F_{n})$-invariant probability measures on the space of $n$-generated marked groups
%J Groups, geometry, and dynamics
%D 2025
%P 431-444
%V 19
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/881/
%R 10.4171/ggd/881
%F 10_4171_ggd_881

Cité par Sources :