Group actions on dendrites and curves

Bruno Duchesne (1) , Nicolas Monod (2)

1 IECL - Institut Élie Cartan de Lorraine
2 EPFL - Ecole Polytechnique Fédérale de Lausanne

We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups. Further results include a Tits alternative and a description of the topological dynamics. We briefly discuss to what extent our results hold for more general topological curves.

Mots clés: dendrites; groups; bounded cohomology; rigidity; curves; dynamics; Tits alternative; lattices

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

Bruno Duchesne, Nicolas Monod. Group actions on dendrites and curves. Annales de l'Institut Fourier, 2018, 68 (5), pp.2277-2309. ⟨10.5802/aif.3209⟩. ⟨hal-01359816v2⟩