One-dimensional actions of Higman's group

Cristóbal Rivas (1) , Michele Triestino (2)

1 USACH - Universidad de Santiago de Chile [Santiago]
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We build a faithful action of Higman's group on the line by homeomorphisms, answering a question of Yves de Cornulier. As a by product we obtain many quasimorphisms from the Higman group into the reals. We also show that every action by C 1-diffeomorphisms of Higman's group on the line or the circle is trivial.

Domaines: Mathématiques [math]; Théorie des groupes [math.GR]; Systèmes dynamiques [math.DS]

Cristóbal Rivas, Michele Triestino. One-dimensional actions of Higman's group. Discrete Analysis, 2019, 20, ⟨10.19086/da.11151⟩. ⟨hal-02121878⟩