Structural properties of dendrite groups

Bruno Duchesne (1) , Nicolas Monod (2)

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

Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many non-isomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metric space has a bounded orbit. In particular they have the fixed point property (FH).

Domaines: Théorie des groupes [math.GR]

Bruno Duchesne, Nicolas Monod. Structural properties of dendrite groups. 2016. ⟨hal-01388407v1⟩